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On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai 2024 University of Arkansas, Fayetteville

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …


Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds 2024 The Graduate Center, City University of New York

Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds

Dissertations, Theses, and Capstone Projects

Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces.

The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed …


Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas 2024 The Graduate Center, City University of New York

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …


Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, Irwan Wijaya Santoso, Daffa Aqila, Rini Riastuti, Rizal Tresna Ramadhani 2024 Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Depok, 16424, Indonesia

Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, Irwan Wijaya Santoso, Daffa Aqila, Rini Riastuti, Rizal Tresna Ramadhani

Journal of Materials Exploration and Findings

In the industrial world, to extend the service life of materials, protection methods are carried out to slow down the material's corrosion rate. The protection method that is often used is the coating method. The coating method is a protection method by coating the substrate material using a coating material to prevent contact between the substrate material and the environment. In this research, the substrate material used is ASTM A36 steel and the coating material used is Surface Tolerant Epoxy paint. The independent variable used in this study lies in the surface preparation method which consists of: solvent cleaning, hand …


Effects Of Ti Addition On The Characteristics Of Al-10zn-6mg-2si/Zro2 Composites Produced By Squeeze Casting, Qesha Diva Prameshvara, Pipin Indah Lestari, Bondan Tiara Sofyan 2024 Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, 16424, Indonesia

Effects Of Ti Addition On The Characteristics Of Al-10zn-6mg-2si/Zro2 Composites Produced By Squeeze Casting, Qesha Diva Prameshvara, Pipin Indah Lestari, Bondan Tiara Sofyan

Journal of Materials Exploration and Findings

Metal matrix composite (MMC) with 7xxx aluminum matrix is potential for ballistic applications due to the combination of strength, toughness, and light weight. Previous study successfully produced aluminum-based composites with SiC particles which were able to stop type III bullet, however cracks remained on back of the plate. Therefore, in this research, SiC was replaced by zirconia (ZrO2) due to its high fracture toughness. Ti-B grain refiner was added to further improve toughness through grain boundary strengthening mechanism. This research developed 5 vol.% ZrO2 strengthened Al-10Zn-6Mg-2Si composite with addition of Al-5Ti-1B grain refiner produced through squeeze casting …


Simulating Cross-Scale Solid-Fluid Interaction Phenomena, Jinyuan Liu 2024 Dartmouth College

Simulating Cross-Scale Solid-Fluid Interaction Phenomena, Jinyuan Liu

Dartmouth College Ph.D Dissertations

Solid-fluid interactions are ubiquitous in nature, and accurate simulation methods are essential for realistic animation, industrial design, and engineering analysis. Com- pared to large-scale coupling phenomena, simulating fine-scale interactions poses extra challenges due to factors such as surface tension, material wettability, and geometric complexity. In this thesis, we pursue novel methodologies to accurately model in- terfacial dynamics between surface-tension fluids and codimensional solids, involving capillary interactions, controllable wettability, and robust contact behaviors. Our ini- tial approach involves developing a novel three-way coupling method, which utilizes a thin liquid membrane, modelled as a simplicial mesh, to facilitate accurate momen- tum transfer, …


Blade Design And Validation Of Hydrokinetic Turbine To Harvest Water Current Energy, Setare Sadeqi 2024 University of New Orleans

Blade Design And Validation Of Hydrokinetic Turbine To Harvest Water Current Energy, Setare Sadeqi

University of New Orleans Theses and Dissertations

The innovative aspect of this research lies in the careful integration of cutting-edge technologies throughout the entire process of designing, fabricating, and testing the carbon fiber propeller for the 3-bladed horizontal axis ocean current turbine (OCT). SolidWorks software played a pivotal role in the initial design phase, enabling a meticulous and precise modeling of the propeller's geometry. The utilization of SolidWorks allowed for a detailed exploration of various design parameters, ensuring that the propeller's structure and form were optimized for performance in ocean current conditions. Moving beyond the realm of virtual design, the choice of carbon fiber as the fabrication …


Towing Tank Trials Of Hydrokinetic Turbine Scale Model To Support Marine Energy System Verification, Shahab Rouhi 2024 University of New Orleans

Towing Tank Trials Of Hydrokinetic Turbine Scale Model To Support Marine Energy System Verification, Shahab Rouhi

University of New Orleans Theses and Dissertations

In response to the escalating demand for sustainable energy solutions and the critical reevaluation of conventional fossil fuels due to environmental concerns, this dissertation embarks on a comprehensive exploration of hydrokinetic energy as a promising alternative. The study delves into the underexplored domain of hydrokinetic energy, leveraging innovative methodologies for effective utilization and harnessing, particularly through the development and investigation of hydrokinetic turbines.

In the realm of hydrokinetic energy conversion, our research has exclusively concentrated on horizontal-axis turbines, distinct from other turbine configurations. Noteworthy is the adaptation of a conventional horizontal-axis wind turbine for water currents, revealing enhanced performance through …


Oscillations Of Capillary Surfaces With Volume And Edge Effects, Dingqian Ding 2024 Clemson University

Oscillations Of Capillary Surfaces With Volume And Edge Effects, Dingqian Ding

All Dissertations

Capillary surfaces are defined by an interface endowed with surface tension that is partially supported by a solid substrate and are susceptible to oscillations reflecting a balance between fluid inertia and the restorative force of surface tension. The wave dynamics strongly depend upon volume change within the domain and edge effects through the boundary conditions applied at the contact-line formed at the liquid-gas-solid interface, while the spatial wave structure conforms to the geometry of the capillary surface. This dissertation develops mathematical models to address these effects for several canonical capillary surfaces, which are organized into two parts that are focused …


Dispersion Of Artificial Tracers In Ventilated Caves, Claudio Pastore, Eric Weber, Frédéric Doumenc, Pierre-Yves Jeannin, Marc Lütscher 2024 Swiss Institute for Speleology and Karst Studies (SISKA), La Chaux-de-Fonds, Switzerland

Dispersion Of Artificial Tracers In Ventilated Caves, Claudio Pastore, Eric Weber, Frédéric Doumenc, Pierre-Yves Jeannin, Marc Lütscher

International Journal of Speleology

Artificial CO2 was used as a tracer along ventilated karst conduits to infer airflow and investigate tracer dispersion. In the karst vadose zone, cave ventilation is an efficient mode of transport for heat, gases and aerosols and thus drives the spatial distribution of airborne particles. Modelling this airborne transport requires geometrical and physical parameters of the conduit system, including the cross-sectional areas, the airflow and average air speed, as well as the longitudinal dispersion coefficient which describes the spreading of a solute. Four gauging tests were carried out in one mine (artificial conduit) and two ventilated caves (natural conduits). …


Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, Temitayo S. Adeyemi 2024 Louisiana State University at Baton Rouge

Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, Temitayo S. Adeyemi

LSU Master's Theses

Reliable prediction of gas migration velocity, void fraction, and length of gas-affected region in water and oil-based muds is essential for effective planning, control, and optimization of drilling operations. However, there is a gap in our understanding of gas behavior and dynamics in water and oil-based muds. This is a consequence of the use of experimental systems that are not representative of field-scale conditions. This study seeks to bridge the gap via the well-scale deployment of distributed fiber-optic sensors for real-time monitoring of gas behavior and dynamics in water and oil-based mud. The aforementioned parameters were estimated in real-time using …


Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, Dwaipayan Sarkar 2024 Western University

Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, Dwaipayan Sarkar

Electronic Thesis and Dissertation Repository

Thermosyphons are enhanced heat transfer devices that can continuously transfer very large amounts of heat rapidly over long distances with small temperature differences. The high heat transfer rate is achieved through simultaneous boiling and condensation of the working fluid and the continuous heat transfer is achieved through recirculation of the working fluid in its liquid and vapor phase. A potentially important application of the thermosyphons has been towards reducing the cycle times of the mold cooling processes which would provide economic incentives to the automotive industry.

Different operational and geometrical parameters such as the input heating power, fill ratio (FR), …


Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw 2024 University of Tennessee, Knoxville

Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw

Faculty Publications and Other Works -- Mathematics

In this second progress report we expand upon our previous report and preliminary work. Specifically, we review some work on the numerical solution of single- and multi-species BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for each species for accurate simulation. …


Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert 2024 Michigan Technological University

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …


Numerical Study Of Owls' Leading-Edge Serrations, Asif Shahriar Nafi, Nikolaos Beratlis, Elias Balaras, Roi Gurka 2023 Coastal Carolina University

Numerical Study Of Owls' Leading-Edge Serrations, Asif Shahriar Nafi, Nikolaos Beratlis, Elias Balaras, Roi Gurka

Physics and Engineering Science

Owls' silent flight is commonly attributed to their special wing morphology combined with wingbeat kinematics. One of these special morphological features is known as the leading-edge serrations: rigid miniature hook-like patterns found at the primaries of the wings' leading-edge. It has been hypothesized that leading-edge serrations function as a passive flow control mechanism, impacting the aerodynamic performance. To elucidate the flow physics associated with owls' leading-edge serrations, we investigate the flow-field characteristic around a barn owl wing with serrated leading-edge geometry positioned at 20° angle of attack for a Reynolds number of 40 000. We use direct numerical simulations, where …


Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, Dona Yuliati, Akhmad Herman Yuwono, Datu Rizal Asral, Donanta Dhaneswara 2023 Universitas Indonesia

Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, Dona Yuliati, Akhmad Herman Yuwono, Datu Rizal Asral, Donanta Dhaneswara

Journal of Materials Exploration and Findings

Hydrocarbon releases might result in serious consequences in various aspects. In addition to the contribution to environmental pollution, repetitive leakages need high repair costs. This study aim is to minimize potential repetitive leakage for other typical 3-phase piping systems. We conducted the risk assessment by adopting Risk Based Inspection (RBI) API 581 to identify risk level, calculating piping lifetime, recommended inspection plan and mitigations. The most relevant root causes can be obtained through quantitative Fault Tree Analysis (FTA). Observation and investigation was taken from eight 3-phase piping systems that experienced repetitive leakages. It has been found that the risk level …


Nitrogen Gas Quenching Pressure Effect On Bs S155 Alloy Steel In Vacuum Furnace, Agus Mulyadi Hasanudin, Eddy Sumarno Siradj 2023 University of Indonesia, Depok

Nitrogen Gas Quenching Pressure Effect On Bs S155 Alloy Steel In Vacuum Furnace, Agus Mulyadi Hasanudin, Eddy Sumarno Siradj

Journal of Materials Exploration and Findings

The production of metal and alloy products requires the use of heat treatment, when during the heat treatment process, quenching is a crucial step. The quenching medium can be anything from water, a salt bath, oil, air and gas. In a vacuum furnace, pressurized gas, most frequently nitrogen (N2) gas, serves as one of the quenching mediums. One of the drawbacks of the quenching process is the distortion and dimensional change of the parts. This paper aims to investigate the influence of nitrogen gas quenching pressure on the distortion and dimensional change of aerospace actuator gear planet parts …


Computational Fluid Dynamics Modeling Of Internal Wave Interactions On Conch Reef, Florida Keys, Megan Miller 2023 Nova Southeastern University

Computational Fluid Dynamics Modeling Of Internal Wave Interactions On Conch Reef, Florida Keys, Megan Miller

All HCAS Student Capstones, Theses, and Dissertations

Internal waves breaking on continental shelves play a significant role in mixing and nutrient delivery to coral reef ecosystems. As internal solitary waves, or solitons, propagate shoreward onto continental slopes, they can become unstable and break into turbulent bores that bring cool, nutrient-rich sub-thermocline water shoreward onto coral reefs. The propagation of turbulent bores generated by internal waves interacting with a complex surface creates high-frequency variabilities in the thermal and nutrient environment of Conch Reef in the Florida Keys, which has been studied previously. Here, I have created a three-dimensional model using ANSYS Fluent Computational Fluid Dynamics (CFD) software to …


Investigating The Effects Of A Southward Flow In The Southeastern Florida Shelf Using Robotic Instruments, Alfredo Quezada 2023 Nova Southeastern University

Investigating The Effects Of A Southward Flow In The Southeastern Florida Shelf Using Robotic Instruments, Alfredo Quezada

All HCAS Student Capstones, Theses, and Dissertations

We deployed a Slocum G3 glider fitted with an acoustic Doppler current profiler (ADCP), a Conductivity-Temperature-Depth sensor (CTD), optics sensor channels, and a propeller on the Southeastern Florida shelf. The ADCP and CTD provide continuous measurements of Northern and Eastern current velocity components, salinity, temperature, and density, throughout the water column in a high-current environment. The optics sensor channels are able to provide measurements of chlorophyll concentrations, colored dissolved organic matter (CDOM), and backscatter particle counts. Additionally, for one of the glider deployments, we deployed a Wirewalker wave-powered profiling platform system also fitted with an ADCP and a CTD in …


Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca 2023 University of New Orleans, New Orleans

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

University of New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …


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