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Articles 1 - 18 of 18
Full-Text Articles in Physics
On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai
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 …
Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps
Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps
Graduate Theses and Dissertations
In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay …
Analysis Of Titan's Fluvial Features Using Numerical Modeling, Jeshurun Horton
Analysis Of Titan's Fluvial Features Using Numerical Modeling, Jeshurun Horton
Mechanical Engineering Undergraduate Honors Theses
River channels have been observed near the Huygens probe landing site on the surface of Titan, along with evidence of rounded water ice boulders transported through fluid flow. Evidence near the landing site suggests active flow of liquid methane, which has motivated the study of the effects of sediment load and channel sizes on Titan’s fluvial features. A numerical model is used to determine the viscosity, flow velocity, and critical boulder transport diameter based on channel size, slope, and a range of sediment concentrations. This model achieves two ends: first, observed boulder diameters are used to determine the ideal channel …
Design And Control Of A Peristaltic Pump To Simulate Left Atrial Pressure In A Conductive Silicone Model, Jeremy Collins
Design And Control Of A Peristaltic Pump To Simulate Left Atrial Pressure In A Conductive Silicone Model, Jeremy Collins
Mechanical Engineering Undergraduate Honors Theses
According to the CDC, atrial fibrillation is responsible for more than 454,000 hospitalizations and approximately 158,000 deaths per year. A common treatment for atrial fibrillation is catheter ablation, a process in which a long flexible tube is guided through the femoral artery and to the source of arrhythmia in the heart, where it measures the electrical potential at various locations and converts problematic heart tissue to scar tissue via ablation. This paper details the design and control of a low-cost ($400) peristaltic pump system using repetitive control to replicate blood pressure in the left atrium in a conductive silicone model …
Development Of A Comsol Microdialysis Model, Towards Creation Of Microdialysis On A Chip With Improved Geometries And Recovery, Patrick Pysz
Development Of A Comsol Microdialysis Model, Towards Creation Of Microdialysis On A Chip With Improved Geometries And Recovery, Patrick Pysz
Graduate Theses and Dissertations
Microdialysis (µD) sampling is a diffusion-limited sampling method that has been widely used in different biomedical fields for greater than 35 years. Device calibration for in vivo studies is difficult for current non-steady state analytes of interest correlated with both inflammatory response and microbial signaling molecules (QS); which exist in low ng/mL to pg/mL with molecular weights over a wide range of 170 Da to 70 kDa. The primary performance metric, relative recovery (RR), relating the collected sample to the extracellular space concentration varies from 10% to 60% per analyte even under controlled bench-top conditions. Innovations in microdialysis device design …
Viscous Liquids And The Glass Transition At Extremely High Pressure: Optical Techniques Applied To Cumene In A Diamond Anvil Cell, Timothy Craig Ransom
Viscous Liquids And The Glass Transition At Extremely High Pressure: Optical Techniques Applied To Cumene In A Diamond Anvil Cell, Timothy Craig Ransom
Graduate Theses and Dissertations
This dissertation presents the results from experiments studying the pressure-dependence of properties associated with the glass transition in the glass-forming liquid cumene. Through the use of a diamond anvil cell, we achieve extremely high pressures over 40,000 atmospheres. A new technique is refined to directly measure the glass transition temperature Tg extremely accurately, and we show that thermodynamic scaling is capable of describing the liquid�glass transition boundary up to record-high pressures. Optical techniques are also implemented to probe the system dynamics in the viscous regime leading up to the glass transition. We present laser light-scattering measurements of the dynamic susceptibility …
Particle Image Velocimetry Design & Installation, Zach Ritchie
Particle Image Velocimetry Design & Installation, Zach Ritchie
Mechanical Engineering Undergraduate Honors Theses
This work will mainly focus on the design, construction, and installation of the Particle Image Velocimetry (PIV) system in the Chemical Hazards Research Center wind tunnel. The PIV system utilizes a Class IV (double pulsed) laser, optics to produce a light sheet, timing circuitry, and a high-resolution camera (with buffered output) to measure a system’s velocity (two-dimensional) field by determining the displacement of particles over the time between laser pulses. For maximum mobility and functionality, the PIV system was installed in the center of the tunnel on a moveable cart with the laser and camera mounted to an adjustable support. …
Electron Shock Waves With A Large Current Behind The Shock Front, H. D. Newberry, M. Hemmati, H. D. Moore, K. Ledbetter, M. W. Bowman
Electron Shock Waves With A Large Current Behind The Shock Front, H. D. Newberry, M. Hemmati, H. D. Moore, K. Ledbetter, M. W. Bowman
Journal of the Arkansas Academy of Science
The propagation of breakdown waves in a gas, which is primarily driven by electron gas pressure, is described by a one-dimensional, steady-state, three-component (electrons, ions, and neutral particles) fluid model. We consider the electron gas partial pressure to be much larger than that of the other species and the waves to have a shock front. Our set of equations consists of the equations of conservation of the flux of mass, momentum, and energy coupled with Poisson’s equation. This set of equations is referred to as the electron fluid dynamical equations. In this study we are considering breakdown waves propagating in …
Characterizing Nanoparticle Size By Dynamic Light Scattering, M. Zaman, S. Ang, S. Singh
Characterizing Nanoparticle Size By Dynamic Light Scattering, M. Zaman, S. Ang, S. Singh
Journal of the Arkansas Academy of Science
The Dynamic Light Scattering (DLS) Technique was used to determine the size, shape and diffusion coefficient of rod-like nanoparticles. The intensity auto-correlation functions of light scattered by particles in a solution were measured and analyzed to obtain the relaxation rates for decay of intensity correlations. These decay rates are related to the diffusion coefficients pertaining to the motion of the particle. In the case of nanorods, there are two types of motion - translational and rotational. By disentangling the relaxation rates, corresponding to these two types of motion, the shape and size of nanoparticles were characterized. These experiments, though limited …
Design And Fabrication Of Nanofluidic Systems With Integrated Sensing Electrodes For Rapid Biomolecule Characterization, Taylor Bradley Busch
Design And Fabrication Of Nanofluidic Systems With Integrated Sensing Electrodes For Rapid Biomolecule Characterization, Taylor Bradley Busch
Graduate Theses and Dissertations
A transparent nanofluidic system with embedded sensing electrodes was designed and fabricated by integrating Atomic Force Microscopy (AFM) nanolithography, Focused Ion Beam (FIB) milling and metal deposition, and standard microfabrication processing. The fabrication process started with the evaporation of chrome/gold (Cr/Au) onto a Pyrex 7740 wafer followed by photolithography and wet etching of the microchannels. The wafer was patterned a second time to form Au microelectrodes with 15-45 micrometer separation gaps in the nanochannel region. Sensing electrodes (up to one micron wide) were then deposited using FIB to bridge the gaps. The nanochannels were realized through both AFM nanolithography and …
Boundary Condition On Electron Temperature For Antiforce Current Bearing Waves, M. Hemmati, W. P. Childs, D. C. Waters, J. D. Counts, J. K. Schmitt
Boundary Condition On Electron Temperature For Antiforce Current Bearing Waves, M. Hemmati, W. P. Childs, D. C. Waters, J. D. Counts, J. K. Schmitt
Journal of the Arkansas Academy of Science
In our investigation of breakdown waves, we apply a one-dimensional, three-component, steady-state fluid model. The wave is considered to be shock fronted and the electrons are assumed to be the main element in propagation of the wave. In our fluid model, the electron gas temperature is assumed to be large enough to sustain the wave motion. Our set of fluid equations is composed of the equations of conservation of mass, momentum and energy plus the Poisson’s equation. This investigation involves breakdown waves for which a large current exist in the vicinity of the wave front. Existence of current behind the …
Electric Discharge: Boundary Conditions, Mostafa Hemmati, Chris Justice
Electric Discharge: Boundary Conditions, Mostafa Hemmati, Chris Justice
Journal of the Arkansas Academy of Science
The electron gas in electric discharge can be described by a set of one-dimensional fluid dynamical equations. The fundamental equations are those of a three-component (electrons, ions, and neutral particles) fluid, different from the treatment of the problem inplasma physics, a fully ionized two-component case. The leading edge of the wave is treated as a shock front driven mainly by the electron gas pressure. Integrating the one-dimensional global differential equations for mass balance, conservation of momentum and energy, and evaluating the constant of integration at the wave front permits derivation of boundary conditions on electron temperature and electron velocity. Using …
Antiforce Wave Profile For Quasi-Neutral Region, Mostafa Hemmati, Pashupati Adhikari, Jeremy Eckart, Marcus Ilbara
Antiforce Wave Profile For Quasi-Neutral Region, Mostafa Hemmati, Pashupati Adhikari, Jeremy Eckart, Marcus Ilbara
Journal of the Arkansas Academy of Science
This article will present a fluid dynamical theory for breakdown waves in which the direction of electric field force on electrons is in the opposite direction of wave propagation. We will refer to such waves as antiforce waves. The set of equations describing the model will include the equation of particle mass balance, equation of conservation of momentum, and equation of conservation of energy, coupled with Poisson's equation. This model treats the potential wave front as an electron shock wave propagating forward mainly due to the electron impact ionization. The shock front is succeeded by a thin dynamical transition region …
Wave Profile For Antiforce Class Ii Waves, Rory Roberts, Mostafa Hemmati
Wave Profile For Antiforce Class Ii Waves, Rory Roberts, Mostafa Hemmati
Journal of the Arkansas Academy of Science
Breakdown waves propagating in the opposite direction of the applied electric field force are referred to as antiforce waves. Breakdown waves moving into a pre-ionized medium are referred to as Class II waves. Using a one-dimensional, steady state, three-fluid, hydrodynamical model and considering the electrons as the main element in propagation of ionizing waves, we have derived the proper boundary conditions for antiforce waves moving into a preionized medium. Using the new boundary conditions and for several current values ahead of the wave, the set of electron fluid dynamical equations (equations of conservation of mass, momentum, and energy coupled with …
Speed Range For Breakdown Waves, Mostafa Hemmati, Eric L. George, Frances Terry
Speed Range For Breakdown Waves, Mostafa Hemmati, Eric L. George, Frances Terry
Journal of the Arkansas Academy of Science
Considering the electrons as the main element in breakdown wave propagation and using a one-dimensional, steady-state, three-fluid, hydrodynamical model, previous investigations have resulted in the completion of a set of equations for conservation of mass, momentum, and energy. We will use the terms proforce and antiforce waves, depending on whether the applied electric field force on electrons is with or against the direction of wave propagation. In the case of antiforce waves, the electron gas temperature and therefore the electron fluid pressure is assumed to be large enough to sustain the wave propagation down the discharge tube. For strong discontinuity …
Proforce Waves: The Effect Of Current Behind The Shock Front On Wave Structure, Mostafa Hemmati, Steven Young
Proforce Waves: The Effect Of Current Behind The Shock Front On Wave Structure, Mostafa Hemmati, Steven Young
Journal of the Arkansas Academy of Science
Recently, the initial boundary conditions for proforce waves with a substantial current behind the shock front have been derived. Computer solutions of the Electron Fluid Dynamical equations meet the expected boundary conditions at the end of the sheath region. This paper will compare the wave structure for proforce waves with and without current behind the shock front.
Computational Fluid Dynamics In Small Airway Models Of The Human Lung, G. Burnside, J. R. Hammersley, Rama N. Reddy, B. Catlin
Computational Fluid Dynamics In Small Airway Models Of The Human Lung, G. Burnside, J. R. Hammersley, Rama N. Reddy, B. Catlin
Journal of the Arkansas Academy of Science
The promise of gene replacement therapy for cystic fibrosis, the administration of drugs via inhalation therapy, and die deposition location of man-made airborne particulates all involve a more complete understanding of the fluid dynamics in the human lung. Flow in the larger airways may be measured through life-sized models directly, but the airways in the peripheral lung are too small and the flows are too complex to be studied in this manner. Computational models can be developed which will accurately represent both the geometric nature of the central airways and the fluid dynamics with in them. Two-dimensional and three-dimensional models …
Measurements Of The Drag On Spheres Falling Through The Air, J. G. Ross, Stephen R. Addison, N.O (Jack) Gaiser
Measurements Of The Drag On Spheres Falling Through The Air, J. G. Ross, Stephen R. Addison, N.O (Jack) Gaiser
Journal of the Arkansas Academy of Science
No abstract provided.