Applied Mathematics Commons^™

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …

(R2102) Chaos Measure In A Discrete Sir Epidemic Model With Constant Recovery, Sonia Aneja, Itendra Kumar, Sada Nand Prasad

Applications and Applied Mathematics: An International Journal (AAM)

A discrete SIR epidemic model with constant recovery and bilinear incidence rate is investigated for emergence of regular and chaotic behaviour in the context of non linear dynamics and different viable settings. The Euler’s discretization method is employed to transform the continuous epidemic model into discrete model which has been used as the study model. Attention is paid to various bifurcation plots obtained by varying certain system parameters while keeping other parameters constant. Bifurcations indicate regular evolution followed by chaos. Regular and chaotic attractors have been drawn in the process. As part of chaos measure, numerical studies are extended to …

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 …

Shevtsov: Growing Pains And Growing Gains: The Arizona Experience, Tynan Lazarus, Jane Shevtsov

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Kreig: Examining Affinity Maturation And Antigenic Drift With An Agent-Based Model, Jasmine Af Kreig, Jannatul Ferdous, Ruian Ke, Ruy M. Ribeiro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bodine: Exploring The Versatility Of Agent-Based Modeling In Netlogo: Lessons From Education And Research, Anne E. Yust

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Development And Testing Of Small-Scale Flash Dryer For Maize Bran, Eden Ngowi

Tanzania Journal of Engineering and Technology (TJET)

Sun drying is the most common technique used to dry various food products due to its economic convenience. However, it is not effective owing to its unreliable nature leading to microbial deterioration and aflatoxin contamination of food. In Tanzania, about 1.3 million tonnes of maize bran are at risk of deterioration annually due to improper drying. The aim of this study was to design, fabricate and test an efficient small-scale flash dryer for maize bran. Using principles of material and energy balance, a small-scale flash dryer with a throughput of 500 kg of dry product per hour was designed resulting …

Assessing The Importance Of Air-Decking Blasting In Controlling Bigv At An Open Pit Gold Mine In Tanzania Using Ann Model, Karim R. Baruti

Tanzania Journal of Engineering and Technology (TJET)

Air-decking blasting technique is used to control blast induced ground vibration (BIGV) in several mines including open-pit gold mines located in Tanzania. While the importance of air-deck to control BIGV is practically evident, theoretical models such as BIGV prediction models cannot be used to assess the importance of air-decking. The main objective of this study was to assess the importance of the air-decking blasting technique to control BIGV using the artificial neural network (ANN)Model. To achieve this objective, ANNs were modeled and trained to learn the pattern of data using Multilayer Perception with Back Propagation to predict BIGV. The main …

Perona-Malik Diffusion-Driven Regularization For Image Resolution Enhancement In Electrical Capacitance Tomography, Nassor Ally

Tanzania Journal of Engineering and Technology (TJET)

Electrical Capacitance Tomography (ECT) is a non-invasive promising method for monitoring industrial processes, such as oil-gas flow in pipelines and solid-gas flow in pneumatic systems. Despite its potential benefits, ECT generates poor-quality images, often used only for qualitative analysis. A non-linear relationship between measured capacitances and permittivity distribution and the ill-posedness of the sensitivity matrix elements causes this limitation. This hinders the applicability of ECT in monitoring online industrial process applications. This work proposes a reconstruction method based on a nonlinear diffusion function to generate high-quality images from the measured capacitance data from the ECT system. The diffusion regularization functional …

Analysis Of The Effect Of Vaccination, Efficient Surveillance And Treatment On The Transmission Dynamics Of Cholera, Loyinmi Adedapo Chris, Ajala Adebisi Shukurat, Alani L. Ijaola

Al-Bahir

In this study, we presented a modified SIR-SI model to investigate the dynamics and potential controls for cholera transmission, with an incident rate equipped with a saturation factor to investigate the combined impact of three vital measures which include effective surveillance, vaccination campaign and proper treatment in case severity. We established among other things, the qualitative analysis of the model to validate the results. Furthermore, the reproduction number (R0) was found to be less than unity (1), through the stability analysis. Additionally, finite different scheme was utilized in solving the differential equations of the model. MATLAB software was used for …

Effects Of A Protection Zone In A Reaction-Diffusion Model With Shifting Bounded Habitat And Allee Effect., Davis Henderson

Electronic Theses and Dissertations

We consider a reaction-diffusion equation that models a population in a shifting bounded habitat with a protection zone and the Allee effect. We assume that the population growth function exhibits the strong Allee effect and has a positive integral within the protection zone (indicating population persistence) and a negative integral in the surrounding patches (indicating population decay). We prove that the existence of steady-state solutions to this system depends on the length of the protection zone. It is demonstrated that there exists some value H* such that, for a protection zone of size H*, there exists a solution and, for …

Frameworks For The Techno-Economic Assessment Of Membrane-Based Bioprocessing Platforms, Juan Jose Romero Conde

All Dissertations

This dissertation describes developing and implementing computational frameworks for simulating and optimizing purification processes in the biopharmaceutical industry. The framework performs techno-economic analyses to establish value propositions for new process alternatives, especially membrane technologies. Initially, the focus is developing a framework capable of simulating monoclonal antibody (mAb) capture using membrane and resin media in multi-column chromatography (MCC) platforms for continuous manufacturing. Subsequently, the impact of capture MCC is compared against other intensification strategies in established mAb manufacturing facilities. Finally, the framework application expands to simulate the purification of adeno-associated virus (AAV) vectors for gene therapy.

Chapter 2 details the framework …

(R2086) Circular Restricted Three-Body Interaction Problem With Various Perturbations, Shiv K. Sahdev, Abdullah .

Applications and Applied Mathematics: An International Journal (AAM)

The motion properties of the infinitesimal body is studied under the forces due to kerr-like oblate heterogeneous primary, continuation fractional potential for secondary, solar sail, three-body interactions, Coriolis and centrifugal forces in the circular restricted three-body problem. The equations of motion of infinitesimal body are evaluated under the above-said perturbations. Using these equations of motion, we illustrate the locations of equilibrium points, their stability, the periodic orbits and Poincaré surfaces of section. This study will applicable on the motion of the artificial satellite.

Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling And Control Of Drug Resistance In Cancer Dynamics, James Greene

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multiscale Modeling Of Microtubule Polarity Mechanisms Following Neuronal Axotomy, Hannah Scanlon

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Comparative Analysis Of Source Identification Algorithms, Pablo A. Curiel

Biology and Medicine Through Mathematics Conference

No abstract provided.

Incorporating Awareness, Misinformation And Optimal Control In A Model Of Sars-Cov-2, Eric Numfor

Biology and Medicine Through Mathematics Conference

No abstract provided.

Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr

Biology and Medicine Through Mathematics Conference

No abstract provided.

Duality Of Ensemble Systems Through Moment Representations, Vignesh Narayanan, Wei Zhang, Jr-Shin Li

Publications

Controlling large-scale dynamic population systems, known as ensemble control, is a pervasive and essential task in many emerging applications from diverse scientific domains. Previous focuses in the area of ensemble control have been placed on seeking open-loop control strategies due to unavailability of state feedback information for each individual system in the ensemble. In this paper, we develop a foundational framework for analysis and control of ensemble systems with closed feedback control loops. We introduce the notion of ensemble moments and construct moment systems associated with the ensemble systems. By extending the classical moment problem in mathematical analysis and statistics, …

Modeling Vibration Stiffness: An Analytical Extension Of Hertzian Theory For Angular Contact Bearings With A Thin Viscoelastic Coating, Davis R. Burton

Honors Theses

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

Electronic Theses and Dissertations

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

System Identification For Motion Control Of Unmanned Aerial Vehicles Platform, Raj Ramesh Agarwal

Theses and Dissertations

Comprehensive research on Unmanned Aerial Vehicles (UAV) system identification for motion control parameters is presented in this thesis, with a focus on the necessity of precise control and improved performance. Using Pseudorandom Binary Sequence (PRBS) and Normally Distributed Random Numbers, it presents a unique technique for excitation of UAV dynamic systems. It also shows how effective random signals are in time-domain identification for precise control in a range of flying circumstances. The piece of research includes a thorough analysis and implementation of various approaches and its further improvements, highlighting the benefits and drawbacks of each. These approaches include the free …

Approximation Via Degree Reduction Of Nonlinearities With Applications To Turbulent Flows, Flame Fronts, And Magnetohydrodynamics, Matthew Enlow

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems." More specifically, in …

Enhanced Post Deposition Annealing Conditions On The Fabrication Of High Quality Thermochromic Vanadium Dioxide Films, Nuru R. Mlyuka

Tanzania Journal of Engineering and Technology (TJET)

Sputter deposition of thermochromic VO2 thin films for smart window applications has been faced with several challenges including the need for high deposition temperature, extremely precise and narrow range of oxygen/argon flow ratio and target poisoning during sputtering. Deposition of VO2 at room temperature without oxygen followed by post-deposition annealing has been cited as one of the potential mitigations to the challenge. In this study, the effects of post-deposition annealing conditions on the structural, electrical and optical properties of VO2 thin films are reported. The films were prepared on soda lime glass substrates using DC magnetron sputtering of metallic vanadium …

Optimal Load Shedding During Service Restoration In Electrical Secondary Distribution Network Based On Reinforcement Learning, Rukia J. Mwifunyi

Tanzania Journal of Engineering and Technology (TJET)

Increased stress in traditional power systems results in blackouts due to voltage instability attributed to a mismatch between available capacity and load demand, especially in distribution networks. Service restoration schemes are designed to return power supply to the affected parts of the networks. The availability of insufficient supply is a complex problem that requires operational experience or an automatic system. The stochastic nature of load demand significantly impacts service restoration as it results in increased restored demand in case a fault occurs during off-peak hours and helps reduce overload if the fault occurs during peak hours. The study adopts an …