Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12

Parametric pattern selection in a reaction-diffusion model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Soot measurements in steady and pulsed ethylene/air diffusion flames using Laser-Induced Incandescence

Combustion-generated carbon black nano particles, or soot, have both positive and negative effects depending on the application. From a positive point of view, it is used as a reinforcing agent in tires, black pigment in inks, and surface coatings. From a negative point of view, it affects performance and durability of many combustion systems, it is a major contributor of global warming, and it is linked to respiratory illness and cancer. Laser-Induced Incandescence (LII) was used in this study to measure soot volume fractions in four steady and twenty-eight pulsed ethylene diffusion flames burning at atmospheric pressure. A laminar coflow diffusion burner combined with a very-high-speed solenoid valve and control circuit provided unsteady flows by forcing the fuel flow with frequencies between 10 Hz and 200 Hz. Periodic flame oscillations were captured by two-dimensional phase-locked LII images and broadband luminosity images for eight phases (0° – 360°) covering each period. A comparison between the steady and pulsed flames and the effect of the pulsation frequency on soot volume fraction in the flame region and the post flame region are presented. The most significant effect of pulsing frequency was observed at 10 Hz. At this frequency, the flame with the lowest mean flow rate had 1.77 times enhancement in peak soot volume fraction and 1.2 times enhancement in total soot volume fraction; whereas the flame with the highest mean flow rate had no significant change in the peak soot volume fraction and 1.4 times reduction in the total soot volume fraction. A correlation (fvRe-1 = a + b·Str) for the total soot volume fraction in the flame region for the unsteady laminar ethylene flames was obtained for the pulsation frequency between 10 Hz and 200 Hz, and the Reynolds number between 37 and 55. The soot primary particle size in steady and unsteady flames was measured using the Time-Resolved Laser-Induced Incandescence (TIRE-LII) and the double-exponential fit method. At maximum frequency (200 Hz), the soot particles were smaller in size by 15% compared to the steady case in the flame with the highest mean flow rate.

Pressure induced structural changes and gas diffusion pathways in monomeric fluorescent proteins

Fluorescent proteins (FPs) are extremely valuable biochemical markers which have found a wide range of applications in cellular and molecular biology research. The monomeric variants of red fluorescent proteins (RFPs), known as mFruits, have been especially valuable for in vivo applications in mammalian cell imaging. Fluorescent proteins consist of a chromophore caged in the beta-barrel protein scaffold. The photophysical properties of an FP is determined by its chromophore structure and its interactions with the protein barrel. Application of hydrostatic pressure on FPs results in the modification of the chromophore environment which allows a systematic study of the role of the protein-chromophore interactions on photophysical properties of FPs. Using Molecular Dynamics (MD) computer simulations, I investigated the pressure induced structural changes in the monomeric variants mCherry, mStrawberry, and Citrine. The results explain the molecular basis for experimentally observed pressure responses among FP variants. It is found that the barrel flexibility, hydrogen bonding interactions and chromophore planarity of the FPs can be correlated to their contrasting photophysical properties at vaious pressures. I also investigated the oxygen diffusion pathways in mOrange and mOrange2 which exhibit marked differences in oxygen sensitivities as well as photostability. Such computational identifications of structural changes and oxygen diffusion pathways are important in guiding mutagenesis efforts to design fluorescent proteins with improved photophysical properties.

Structural flexibility and oxygen diffusion pathways in monomeric fluorescent proteins

Fluorescent proteins are valuable tools as biochemical markers for studying cellular processes. Red fluorescent proteins (RFPs) are highly desirable for in vivo applications because they absorb and emit light in the red region of the spectrum where cellular autofluorescence is low. The naturally occurring fluorescent proteins with emission peaks in this region of the spectrum occur in dimeric or tetrameric forms. The development of mutant monomeric variants of RFPs has resulted in several novel FPs known as mFruits. Though oxygen is required for maturation of the chromophore, it is known that photobleaching of FPs is oxygen sensitive, and oxygen-free conditions result in improved photostabilities. Therefore, understanding oxygen diffusion pathways in FPs is important for both photostabilites and maturation of the chromophores. We used molecular dynamics calculations to investigate the protein barrel fluctuations in mCherry, which is one of the most useful monomeric mFruit variants, and its GFP homolog citrine. We employed implicit ligand sampling and locally enhanced sampling to determine oxygen pathways from the bulk solvent into the mCherry chromophore in the interior of the protein. The pathway contains several oxygen hosting pockets, which were identified by the amino acid residues that form the pocket. We calculated the free-energy of an oxygen molecule at points along the path. We also investigated an RFP variant known to be significantly less photostable than mCherry and find much easier oxygen access in this variant. We showed that oxygen pathways can be blocked or altered, and barrel fluctuations can be reduced by strategic amino acid substitutions. The results provide a better understanding of the mechanism of molecular oxygen access into the fully folded mCherry protein barrel and provide insight into the photobleaching process in these proteins.

Soot Measurements in Steady and Pulsed Ethylene/Air Diffusion Flames Using Laser-Induced Incandescence

Combustion-generated carbon black nano particles, or soot, have both positive and negative effects depending on the application. From a positive point of view, it is used as a reinforcing agent in tires, black pigment in inks, and surface coatings. From a negative point of view, it affects performance and durability of many combustion systems, it is a major contributor of global warming, and it is linked to respiratory illness and cancer. Laser-Induced Incandescence (LII) was used in this study to measure soot volume fractions in four steady and twenty-eight pulsed ethylene diffusion flames burning at atmospheric pressure. A laminar coflow diffusion burner combined with a very-high-speed solenoid valve and control circuit provided unsteady flows by forcing the fuel flow with frequencies between 10 Hz and 200 Hz. Periodic flame oscillations were captured by two-dimensional phase-locked LII images and broadband luminosity images for eight phases (0°- 360°) covering each period. A comparison between the steady and pulsed flames and the effect of the pulsation frequency on soot volume fraction in the flame region and the post flame region are presented. The most significant effect of pulsing frequency was observed at 10 Hz. At this frequency, the flame with the lowest mean flow rate had 1.77 times enhancement in peak soot volume fraction and 1.2 times enhancement in total soot volume fraction; whereas the flame with the highest mean flow rate had no significant change in the peak soot volume fraction and 1.4 times reduction in the total soot volume fraction. A correlation (ƒv Reˉ1 = a+b· Str) for the total soot volume fraction in the flame region for the unsteady laminar ethylene flames was obtained for the pulsation frequency between 10 Hz and 200 Hz, and the Reynolds number between 37 and 55. The soot primary particle size in steady and unsteady flames was measured using the Time-Resolved Laser-Induced Incandescence (TIRE-LII) and the double-exponential fit method. At maximum frequency (200 Hz), the soot particles were smaller in size by 15% compared to the steady case in the flame with the highest mean flow rate.

Longitudinal diffusion tensor imaging in dementia with Lewy bodies and Alzheimer's disease

Copyright © 2016 Elsevier Ltd. All rights reserved. Acknowledgements The study was supported by the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Cambridge University Hospitals NHS Foundation Trust and the University of Cambridge, and the NIHR Biomedical Research Unit in Dementia and the Biomedical Research Centre awarded to Newcastle upon Tyne Hospitals NHS Foundation Trust and Newcastle University. Elijah Mak was in receipt of a Gates Cambridge PhD studentship.

Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Solvation Structure of Uracil in Ionic Liquids

The local solvation environment of uracil dissolved in the ionic liquid 1-ethyl-3-methylimidazolium acetate has been studied using neutron diffraction techniques. At solvent:solute ratios of 3:1 and 2:1 ionic liquid:uracil, little perturbation of the ion-ion correlations compared to those of the neat ionic liquid are observed. We find that solvation of the uracil is driven predominantly by the acetate anion of the solvent. While short distance correlations exist between uracil and the imidazolium cation, the geometry of these contacts suggest that they cannot be considered as hydrogen bonds, in contrast to other studies by Araújo et al. (J. M. Araújo, A. B. Pereiro, J. N. Canongia-Lopes, L. P. Rebelo, I. M. Marrucho, J. Phys. Chem. B 2013, 117, 4109-4120). Nevertheless, this combination of interactions of the solute with both the cation and anion components of the solvents helps explain the high solubility of the nucleobase in this media. In addition, favorable uracil-uracil contacts are observed, of similar magnitude to those between cation and uracil, and are also likely to aid dissolution