Effective Boundary Conditions for the Fisher-KPP Equation on a Domain with 3-dimensional Optimally Aligned Coating

We consider the Fisher-KPP equation on a three-dimensional domain surrounded by a thin layer whose diffusion rates are drastically different from that in the bulk. The bulk is isotropic, while the layer is considered to be anisotropic and ``optimally aligned", where the normal direction is always an eigenvector of the diffusion tensor. To see the effect of the layer, we derive effective boundary conditions (EBCs) by the limiting solution of the Fisher-KPP equation as the thickness of the layer shrinks to zero. These EBCs contain some exotic boundary conditions including the Dirichlet-to-Neumann mapping and the Fractional Laplacian. Moreover, we emphasize that each EBC keeps effective indefinitely, even as time approaches infinity.Comment: 19 pages, 1 figure. arXiv admin note: text overlap with arXiv:2301.1365

Proteins at Interfaces: Conformational Behavior and Wear

Proteins at interfaces play a major role in biomaterials and lab-on-a-chip devices. Protein interactions with the surface change their conformations and therefore their ability to bind to their respective ligands. Another major area of interest surrounding biomaterials and lab-on-a-chip devices is the prediction and prevention of wear. Wear is the progressive loss of material from an object caused by contact and relative movement of the contacting solid, liquid, or gas. It is estimated that wear costs 1% of the gross domestic product (approximately $150 billion for the US). With the emergence of drug-releasing implants and lab-on-the-chip devices, wear has also become a major concern in bio- and nano- technology. In our laboratory, we use microtubules (filamentous proteins) gliding on kinesin motor proteins as transporters in biosensors. This system, known as the motility assay, is ideal for studying how the conformation of kinesins impacts the gliding of microtubules and therefore the performance of the biosensor. The proposed studies seek to show that kinesins' geometry changes with their grafting density following De Gennes' scaling laws for flexible polymers (Chapter 2 , published in Langmuir as E.L.P. Dumont, H. Belmas, and H. Hess, Observing the mushroom-to-brush transition for kinesin proteins, 2013, 29 (49), 15142-15145) and that microtubules experience molecular wear due to their repeated interactions with kinesins (Chapter 3, under review for Nature Nanotechnology as E.L.P. Dumont and H. Hess, Molecular wear of microtubules propelled by surface-adhered kinesins). These two results permit the prediction of the lifetime of biosensors using kinesin-propelled microtubules (Chapter 4, to be submitted to Nano Letters as Y. Jeune-Smith, E.L.P. Dumont and H. Hess, Wear and breakage combine to mechanically degrade kinesin-powered molecular shuttles). I also discuss the importance of mechanical fatigue for molecular machine design (Chapter 5, published as H. Hess and E.L.P. Dumont, Fatigue Failure and Molecular Machine Design, Small, 7, 1619-1623, 2011). Finally, and it is unrelated to the previous chapters, I developed Monte Carlo simulations for protein adsorption on polymer-coated surfaces (Chapter 6, to be submitted as E.L.P. Dumont, A.V. Guillaume, A. Gore, and H. Hess, Random Sequential Adsorption of proteins on polymer-covered surfaces: A simulation-based approach) and I explored a molecular model to explain the fracture of materials at low stresses (Chapter 7)

Dielectrophoresis of colloids and polyelectrolytes

This PhD dissertation describes experimental and theoretical investigations on the dielectrophoretic movement of colloidal particles and polyelectrolytes suspended in aqueous solution. Dielectrophoresis (DEP) is the movement of polarisable particles in non-uniform electric fields according to their induced, or effective, polarisability. The colloidal particles used in experiments were fluorescently labelled 216 nm diameter carboxyl-modified polystyrene micro-spheres (beads) and the polyelectrolyte particles were fluorescently labelled 12 kilobase pair DNA plasmids with approximately 1 gm planar diameter. The dielectrophoretic force was generated by applying electrical alternating current (AC) potentials of varying frequency to micro-fabricated electrodes covered with low conductivity aqueous suspending media. The electrodes used for quantitative particle measurements were interdigitated Ti/Pd/Au electrode arrays (10 μm width and 10 μm gap) microfabricated on glass microscope slides using standard photolithography techniques. The frequency dependent effective particle polarisability, ap, is a key parameter in governing the dielectrophoretic force. Time domain dielectric spectroscopic measurements of solutions of DNA gave values of ap at 2 to 80x 10"31 (F m2), in the frequency range 12 MHz - 140 kHz. For latex micro-spheres, the DEP cross-over technique was used to predict ap. Since the diameters of micro-spheres and plasmid DNA were up to a micron in size, their movement in an aqueous medium at room temperature was influenced by random, thermal Brownian motion. One and two-dimensional Fokker-Planck equation (FPE) models were constructed to predict DEP-driven collection of particles onto electrodes. The model comprised DEP-induced particle flux and thermally driven diffusion flux. The FPE computer model also predicted the diffusion of particles away from the electrode surfaces after the DEP force was switched off, called particle relaxation. Using the values of ap, the FPE model was used to simulate particle collections and relaxations under the action of DEP onto a planar interdigitated electrode surface for a range of applied frequencies and voltages. The collection of particles (beads and plasmid DNA) onto interdigitated electrodes was observed using epi-fluorescence microscopy together with video-recording of images. The images were processed using software written in MATLAB 5.0. The processed images yielded timedependent particle collection profiles representing particle accumulation on the electrodes, and particle relaxation profiles after the DEP potential was switched off. Theoretical predictions were used to compare DEP collection experiments of 216 nm diameter beads and DNA plasmids. Collection and relaxation profiles were measured for AC frequencies from 100 kHz to 20 MHz and applied voltages from 1 to 4.5 V (peak). The data was in broad agreement with theoretical predictions, but there were significant quantitative differences. There are a number of reasons for these discrepancies between theory and experiment. These include electrohydrodynamically induced fluid motion that can disturb particle movement, and distortion of the electric field generated by the interdigitated electrodes due to the presence of charges associated with colloidal particles and DNA. As a first approximation, these factors were not included in the FPE model

Efficient and Open-Source Tool for the Prediction of Thermowell Structural Response

Thermowells are widely used in the aid of the measurement of temperature in high velocity or corrosive flow in large industrial installations. They are susceptible to vortex induced vibration which can be a cause of two types of damage; fatigue failure and resonance failure. Hence it is important to understand the mechanisms that may avoid vortex induced vibration as failure of a thermowell can cause a leak in the pipe or vessel it is installed on. An industry standard for the sizing and installation of a thermowell in order to avoid failure due to vortex induced vibration, hydrostatic pressure or static bending already exists. The standard is thorough and has been amended as recently as 2016 in order to increase safety in working with thermowells. However, it has its shortcomings with some assumptions it makes and when considering unique designs. A unique design of particular interest from industry is that of a cylindrical well with helical strakes attached. This affects the boundary layer of the fluid on the thermowell.In this work, a novel tool is developed for computing the structural response of a thermowell depending on the flow environment in which it is placed in. The tool exploits one-way coupling requiring the physics of fluid flow and solid dynamics. The incompressible Navier-Stokes equations with a RANS turbulence model and a structural modal superposition method are used to solve for the fluid and the solid. An experimental setup was also proposed with the purpose of benchmarking the numerical approach, however, experimental testing was not pursued.The numerical model showed a significant reduction in time dynamic oscillatory force being applied to the thermowell when helical strakes are introduced but an increase in steady state force. Therefore, with the presence of helical strakes, the dynamics stress levels that the thermowell experiences is reduced making the thermowell less susceptible to failure

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Multi-dimensional modeling and simulation of semiconductor nanophotonic devices

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources

Growth of low disorder GaAs/AlGaAs heterostructures by molecular beam epitaxy for the study of correlated electron phases in two dimensions

The unparalleled quality of GaAs/AlGaAs heterostructures grown by molecular beam epitaxy has enabled a wide range of experiments probing interaction effects in two-dimensional electron and hole gases. This dissertation presents work aimed at further understanding the key material-related issues currently limiting the quality of these 2D systems, particularly in relation to the fractional quantum Hall effect in the 2nd Landau level and spin-based implementations of quantum computation.^ The manuscript begins with a theoretical introduction to the quantum Hall effect which outlines the experimental conditions necessary to study the physics of interest and motivates the use of the semiconductor growth and cryogenic measurement techniques outlined in chapters 2 and 3, respectively. In addition to a generic introduction to the molecular beam epitaxy growth technique, chapter 2 summarizes some of what was learned about the material purity issues currently limiting the low temperature electron mobility. Finally, a series of appendices are included which detail the experimental methods used over the course of the research.^ Chapter 4 presents an experiment examining transport in a low density two-dimensional hole system in which the hole density could be varied by means of an evaporated back gate. At low temperature, the mobility reached a maximum of 2.6 × 106 cm2/Vs at a density of 6.2 × 1010 cm-2 which is the highest reported mobility in a two-dimensional hole system to date. In addition, it was found that the mobility as a function of density did not follow a power law with a single exponent. Instead, it was found that the power law varied with density, indicating a cross-over between dominant scattering mechanisms at low density and high density. At low density the mobility was found to be limited by remote ionized impurity scattering, while at high density the dominant scattering mechanism was found to be background impurity scattering.^ Chapter 5 details an experiment examining transport in a series of two-dimensional hole gases in which the dopant setback distance and the Al mole fraction in the barriers of the quantum well were varied. The hole density was tuned in this way from 0.18 – 1.9 × 1011 cm-2. Surprisingly, the mobility at T = 0.3 K was found to peak at 2.3 × 10 6 cm-2at an intermediate density of 6.5 × 10 10 cm-2. Self-consistent Schrödinger/Poisson calculations were performed for each wafer to examine the scattering rates due to a variety of potentials at low temperature. The drop in mobility at high density could be accounted for with the inclusion of interface roughness scattering, but using the same interface roughness scattering parameters for similar two-dimensional electron gases produced inconsistent results. This leaves open the possibility of contributions from other scattering mechanisms in the hole samples at high density.^ Chapter 6 presents an in-depth study of in-situ backgated two-dimensional gases used for studying the fragile fractional quantum Hall states in the 2nd Landau level. It was found that leakage currents as small as 4 pA could cause noticeable heating of the electron gas if the lattice was not properly thermally anchored to the cryostat. However, it was also found that when the heterostructure design and device fabrication recipe were properly optimized, gate voltages as large as 4 V could be applied before the leakage turned on, allowing the density to be tuned from full depletion to over 4 × 1011 cm-2. As a result, heating effects at dilution refrigerator temperatures were negligible and the gap at ν = 5/2 could be tuned continuously with density to a maximum value of 625 mK, the largest reported to date. An unusual evolution of the reentrant integer quantum Hall states as a function of density is also reported. Such devices should prove useful for the study of electron correlations in nanostructures in the 2nd Landau level