Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

In vitro micro propagation of Nicotiana benthamiana via axillary shoots

Axillary shoots of Nicotiana benthamiana were regenerated from nodal explants in two weeks using MS media supplemented with the cytokinin, kinetin (0.5 mg/L), and the auxin, indole-3-butyric acid (IBA) (0.1 mg/L). Ninety two percent of shoots were 2.1-20 mm tall, a size ideal for root induction. After transfer to hormone-free MS they readily produced roots within seven days, with phenotypically normal, fully developed plants being obtained within four weeks. Leaf chlorosis due to iron deficiency was observed in plants over time, however, this was overcome by doubling the concentration of inorganic iron. This rapid micro-propagation system is particularly useful for the in vitro mass production of N. benthamiana plants for various biotechnological applications.

Fiber Bragg grating accelerometer based on a transversely rotating stick

Fiber Bragg Grating (FBG) accelerometers using transverse forces with an inertial object placed at the middle of the FBG have a high sensitivity but low resonant frequency. The resonant frequency 26 Hz and sensitivity at 6 Hz 1.29 nm/g were reported based on a 50mm-long FBG accelerometer. We demonstrate that the first FBG accelerometer based on a transversely rotating stick, which can, at the same or even larger size, keep the high sensitivity and significantly increase the low resonant frequency. In our experiments, a 77.5mm-long FBG accelerometer has achieved a similar sensitivity but 65% higher resonant frequency. This novel structure not only significantly widens the potential applications of FBG accelerometers by increasing their resonant frequencies but also provides a new route to design other accelerometers, e.g. micro accelerometers.

Mapping bound plasmon propagation on a nanoscale stripe waveguide using quantum dots: Influence of spacer layer thickness

In this paper we image the highly confined long range plasmons of a nanoscale metal stripe waveguide using quantum emitters. Plasmons were excited using a highly focused 633 nm laser beam and a specially designed grating structure to provide stronger incoupling to the desired mode. A homogeneous thin layer of quantum dots was used to image the near field intensity of the propagating plasmons on the waveguide. We observed that the photoluminescence is quenched when the QD to metal surface distance is less than 10 nm. The optimised spacer layer thickness for the stripe waveguides was found to be around 20 nm. Authors believe that the findings of this paper prove beneficial for the development of plasmonic devices utilising stripe waveguides.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

From “somatic scandals” to “a constant potential for violence”? The culture of dissection, brain-based learning, and the rewriting/rewiring of “the child”

This article analyzes the “messy and numberless beginnings” of the hope placed upon neurological foundationalism to provide a solution to the “problem” of differences between students and to the achievement of educational goals. Rather than arguing for or against educational neuroscience, the article moves through five levels to examine the conditions of possibility for subscribing to the brain as a causal organological locus of learning.

Fatigue crack propagation analysis of plaque rupture

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

Robust estimation using the Huber function with a data-dependent tuning constant

Robust estimation often relies on a dispersion function that is more slowly varying at large values than the square function. However, the choice of tuning constant in dispersion functions may impact the estimation efficiency to a great extent. For a given family of dispersion functions such as the Huber family, we suggest obtaining the "best" tuning constant from the data so that the asymptotic efficiency is maximized. This data-driven approach can automatically adjust the value of the tuning constant to provide the necessary resistance against outliers. Simulation studies show that substantial efficiency can be gained by this data-dependent approach compared with the traditional approach in which the tuning constant is fixed. We briefly illustrate the proposed method using two datasets.

Achilles tendon loading patterns during barefoot walking and slow running on a treadmill: An ultrasonic propagation study

Measurement of tendon loading patterns during gait is important for understanding the pathogenesis of tendon "overuse" injury. Given that the speed of propagation of ultrasound in tendon is proportional to the applied load, this study used a noninvasive ultrasonic transmission technique to measure axial ultrasonic velocity in the right Achilles tendon of 27 healthy adults (11 females and 16 males; age, 26 ± 9 years; height, 1.73 ± 0.07 m; weight, 70.6 ± 21.2 kg), walking at self-selected speed (1.1 ± 0.1 m/s), and running at fixed slow speed (2 m/s) on a treadmill. Synchronous measures of ankle kinematics, spatiotemporal gait parameters, and vertical ground reaction forces were simultaneously measured. Slow running was associated with significantly higher cadence, shorter step length, but greater range of ankle movement, higher magnitude and rate of vertical ground reaction force, and higher ultrasonic velocity in the tendon than walking (P < 0.05). Ultrasonic velocity in the Achilles tendon was highly reproducible during walking and slow running (mean within-subject coefficient of variation < 2%). Ultrasonic maxima (P1, P2) and minima (M1, M2) were significantly higher and occurred earlier in the gait cycle (P1, M1, and M2) during running than walking (P < 0.05). Slow running was associated with higher and earlier peaks in loading of the Achilles tendon than walking.

Power system stability implications from electromechanical wave propagation

Electromechanical wave propagation characterizes the first-swing dynamic response in a spatially delayed manner. This paper investigates the characteristics of this phenomenon in two-dimensional and one-dimensional power systems. In 2-D systems, the wave front expands as a ripple in a pond. In 1-D systems, the wave front is more concentrated, retains most of its magnitude, and travels like a pulse on a string. This large wave front is more impactful upon any weak link and easily causes transient instability in 1-D systems. The initial disturbance injects both high and low frequency components, but the lumped nature of realistic systems only permits the lower frequency components to propagate through. The kinetic energy split at a junction is equal to the generator inertia ratio in each branch in an idealized continuum system. This prediction is approximately valid in a realistic power system. These insights can enhance understanding and control of the traveling waves.

Finite element modelling of lamb wave propagation in prestress concrete and effect of the prestress force on the wave’s characteristic

In order to assess the structural reliability of bridges, an accurate and cost effective Non-Destructive Evaluation (NDE) technology is required to ensure their safe and reliable operation. Over 60% of the Australian National Highway System is prestressed concrete (PSC) bridges according to the Bureau of Transport and Communication Economics (1997). Most of the in-service bridges are more than 30 years old and may experience a heavier traffic load than their original intended level. Use of Ultrasonic waves is continuously increasing for (NDE) and Structural Health Monitoring (SHM) in civil, aerospace, electrical, mechanical applications. Ultrasonic Lamb waves are becoming more popular for NDE because it can propagate long distance and reach hidden regions with less energy loses. The purpose of this study is to numerically quantify prestress force (PSF) of (PSC) beam using the fundamental theory of acoustic-elasticity. A three-dimension finite element modelling approach is set up to perform parametric studies in order to better understand how the lamb wave propagation in PSC beam is affected by changing in the PSF level. Results from acoustic-elastic measurement on prestressed beam are presented, showing the feasibility of the lamb wave for PSF evaluation in PSC bridges.