Stochastic dynamics in periodic potentials

This thesis describes the dynamics of both electrons and atoms in periodic potentials. In particular, it explores how such potentials can be used to realise a new type of quantum chaos in which the effective classical Hamiltonian originates from the intrinsically quantum nature of energy bands. Firstly, this study examines electron dynamics in a superlattice with an applied voltage and a tilted magnetic field. This system displays a rare type of chaos known as non-KAM (Kolmogorov-Arnold-Moser) chaos, which switches on abruptly when an applied perturbation reaches certain critical values. The onset of chaos in the system leads to the formation of complex patterns in phase space known as stochastic webs. The electron behaviour under these conditions is analysed both semiclassically and quantum mechanically, and the results compared to experimental studies. We show that the presence of stochastic webs strongly enhances electron transport. We calculate Wigner functions of the electron wavefunction at various times and show that, when compared to the Poincare sections, evidence of stochastic web formation is observed in the quantum mechanical phase space. Two designs of superlattice are studied and we show, in a full quantum mechanical analysis, that the design of the superlattice has a pronounced effect on the probability of inter-miniband tunnelling and hence the calculated and measured transport characteristics. Secondly, we explore the dynamics of an ultra-cold sodium atom falling through an optical lattice whilst confined in a harmonic gutter potential that is tilted at an angle to the lattice axis. We show this system is analogous to the case of an electron in a superlattice, and that the atomic dynamics show similar enhanced transport properties for certain trapping frequencies. We also find that in a full quantum mechanical calculation, the atomic wavepacket tends to fragment as the angle at which the gutter potential is tilted is increased. Finally, we examine the dynamics of a Bose-Einstein condensate falling through an optical lattice whilst confined in a harmonic gutter potential. We vary the strength of the interatomic interaction parameter to investigate the role of interactions in the system and find that, even for small tilt angles, the condensate wavefunction fragments. For large interaction parameters combined with large tilt angles, the wavefunction explodes catastrophically

Stochastic dynamics in periodic potentials

This thesis describes the dynamics of both electrons and atoms in periodic potentials. In particular, it explores how such potentials can be used to realise a new type of quantum chaos in which the effective classical Hamiltonian originates from the intrinsically quantum nature of energy bands. Firstly, this study examines electron dynamics in a superlattice with an applied voltage and a tilted magnetic field. This system displays a rare type of chaos known as non-KAM (Kolmogorov-Arnold-Moser) chaos, which switches on abruptly when an applied perturbation reaches certain critical values. The onset of chaos in the system leads to the formation of complex patterns in phase space known as stochastic webs. The electron behaviour under these conditions is analysed both semiclassically and quantum mechanically, and the results compared to experimental studies. We show that the presence of stochastic webs strongly enhances electron transport. We calculate Wigner functions of the electron wavefunction at various times and show that, when compared to the Poincare sections, evidence of stochastic web formation is observed in the quantum mechanical phase space. Two designs of superlattice are studied and we show, in a full quantum mechanical analysis, that the design of the superlattice has a pronounced effect on the probability of inter-miniband tunnelling and hence the calculated and measured transport characteristics. Secondly, we explore the dynamics of an ultra-cold sodium atom falling through an optical lattice whilst confined in a harmonic gutter potential that is tilted at an angle to the lattice axis. We show this system is analogous to the case of an electron in a superlattice, and that the atomic dynamics show similar enhanced transport properties for certain trapping frequencies. We also find that in a full quantum mechanical calculation, the atomic wavepacket tends to fragment as the angle at which the gutter potential is tilted is increased. Finally, we examine the dynamics of a Bose-Einstein condensate falling through an optical lattice whilst confined in a harmonic gutter potential. We vary the strength of the interatomic interaction parameter to investigate the role of interactions in the system and find that, even for small tilt angles, the condensate wavefunction fragments. For large interaction parameters combined with large tilt angles, the wavefunction explodes catastrophically

Hand and torso pre-cooling does not enhance subsequent high-intensity cycling or cognitive performance in heat

The purpose of this study was to compare the separate and combined effects of two practical cooling methods (hand and torso) used prior to exercise on subsequent high-intensity cycling performance in heat. Ten trained male cyclists (V̇O2peak: 65.7 ± 10.7 ml.kg−1.min−1) performed four experimental trials (randomised within-subjects design) involving 30-min of pre-cooling (20-min seated; PRE-COOL, 10 min warm-up; PRE-COOL+WUP), while using a: (1) hand-cooling glove (CG); (2) cooling jacket (CJ); (3) both CG and CJ (CG+J); or (4) no-cooling (NC) control, followed by a cycling race simulation protocol (all performed in 35.0 ± 0.6°C and 56.6 ± 4.5% RH). During the 30-min of pre-cooling, no reductions in core (Tc) or mean skin temperature (Tsk) occurred; however, Tsk remained lower in the CJ and CG+J trials compared to NC and CG (p = 0.002–0.040, d= 0.55–1.01). Thermal sensation ratings also indicated that participants felt “hotter” during NC compared to all other trials during both PRE-COOL and PRE-COOL+WUP (p = 0.001–0.015, d= 1.0–2.19), plus the early stages of exercise (sets 1–2; p = 0.005–0.050, d= 0.56–1.22). Following cooling, no differences were found for absolute Tc and Tsk responses between trials over the entire exercise protocol (p > 0.05). Exercise and cognitive (working memory) performance also did not differ between trials (p = 0.843); however, cognitive performance improved over time in all trials (p < 0.001). In summary, pre-cooling (20-min seated and 10-min warm-up) in heat did not improve subsequent high-intensity cycling performance, cognitive responses and associated thermoregulatory strain (Tc and Tsk) compared to control

Resonance line-profile calculations based on hydrodynamical models of cataclysmic variable winds

We present synthetic line profiles as predicted by the models of 2-D line- driven disk winds due to Proga, Stone & Drew. We compare the model line profiles with HST observations of the cataclysmic variable IX Vel. The model wind consists of a slow outflow that is bounded on the polar side by a fast stream. We find that these two components of the wind produce distinct spectral features. The fast stream produces profiles which show features consistent with observations. These include the appearance of the P-Cygni shape for a range of inclinations, the location of the maximum depth of the absorption component at velocities less than the terminal velocity, and the transition from absorption to emission with increasing inclination. However the model profiles have too little absorption or emission equivalent width. This quantitative difference between our models and observations is not a surprise because the line-driven wind models predict a mass loss rate that is lower than the rate required by the observations. We note that the model profiles exhibit a double-humped structure near the line center which is not echoed in observations. We identify this structure with a non-negligible redshifted absorption which is formed in the slow component of the wind where the rotational velocity dominates over expansion velocity. We conclude that the next generation of disk wind models, developed for application to CVs, needs to yield stronger wind driving out to larger disk radii than do the present models.Comment: LaTeX, 19 pages, to appear in Ap

Matched increases in cerebral artery shear stress, irrespective of stimulus, induce similar changes in extra-cranial arterial diameter in humans.

The mechanistic role of arterial shear stress in the regulation of cerebrovascular responses to physiological stimuli (exercise and hypercapnia) is poorly understood. We hypothesised that, if shear stress is a key regulator of arterial dilation, then matched increases in shear, induced by distinct physiological stimuli, would trigger similar dilation of the large extra-cranial arteries. Participants ( n = 10) participated in three 30-min experimental interventions, each separated by ≥48 h: (1) mild-hypercapnia (FICO2:∼0.045); (2) submaximal cycling (EX; 60%HRreserve); or (3) resting (time-matched control, CTRL). Blood flow, diameter, and shear rate were assessed (via Duplex ultrasound) in the internal carotid and vertebral arteries (ICA, VA) at baseline, during and following the interventions. Hypercapnia and EX produced similar elevations in blood flow and shear rate through the ICA and VA ( p < 0.001), which were both greater than CTRL. Vasodilation of ICA and VA diameter in response to hypercapnia (5.3 ± 0.8 and 4.4 ± 2.0%) and EX (4.7 ± 0.7 and 4.7 ± 2.2%) were similar, and greater than CTRL ( p < 0.001). Our findings indicate that matched levels of shear, irrespective of their driving stimulus, induce similar extra-cranial artery dilation. We demonstrate, for the first time in humans, an important mechanistic role for the endothelium in regulating cerebrovascular response to common physiological stimuli in vivo

Acute impact of conventional and eccentric cycling on platelet and vascular function in patients with chronic heart failure.

Evidence-based guidelines recommend exercise therapy for patients with chronic heart failure (CHF). Such patients have increased atherothrombotic risk. Exercise can transiently increase platelet activation and reactivity and decrease vascular function in healthy participants, although data in CHF is scant. Eccentric (ECC) cycling is a novel exercise modality which may be particularly suited to patients with CHF, but the acute impacts of ECC on platelet and vascular function are currently unknown. Our null hypothesis was that ECC and concentric (CON) cycling, performed at matched external workloads, would not induce changes in platelet or vascular function in patients with CHF. Eleven patients with heart failure with reduced ejection fraction (HFrEF) took part in discrete bouts of ECC and CON cycling. Before and immediately after exercise, vascular function was assessed by measuring diameter and flow mediated dilation (FMD) of the brachial artery. Platelet function was measured by the flow cytometric determination of glycoprotein IIb/IIIa activation and granule exocytosis in the presence and absence of platelet agonists. ECC increased baseline artery diameter (pre: 4.0±0.8mm vs post: 4.2±0.7mm, P=0.04) and decreased FMD%. When changes in baseline artery diameter were accounted for the decrease in FMD post-ECC was no longer significant. No changes were apparent after CON. Neither ECC nor CON resulted in changes to any platelet function measures (all P>0.05). These results suggest both ECC and CON cycling at a moderate intensity and short duration can be performed by patients with HFrEF, without detrimental impacts on vascular or platelet function

Morning exercise mitigates the impact of prolonged sitting on cerebral blood flow in older adults

Preventing declines in cerebral blood flow is important for maintaining optimal brain health with aging. We compared the effects of a morning bout of moderate-intensity exercise, with and without subsequent light-intensity walking breaks from sitting, on cerebral blood velocity over 8 h in older adults. In a randomized crossover trial, overweight/obese older adults (n = 12, 70 ± 7 yr; 30.4 ± 4.3 kg/m2), completed three acute conditions (6-day washout); SIT: prolonged sitting (8 h, control); EX+SIT: sitting (1 h), moderate-intensity walking (30 min), followed by uninterrupted sitting (6.5 h); and EX + BR: sitting (1 h), moderate-intensity walking (30 min), followed by sitting (6.5 h) interrupted with 3 min of light-intensity walking every 30 min. Bilateral middle cerebral artery velocities (MCAv) were determined using transcranial Doppler at 13 time points across the day. The temporal pattern and average MCAv over 8 h was determined. The pattern of MCAv over 8 h was a negative linear trend in SIT (P < 0.001), but a positive quadratic trend in EX + SIT (P < 0.001) and EX + BR (P < 0.01). Afternoon time points in SIT were lower than baseline within condition (P ≤ 0.001 for all). A morning dip in MCAv was observed in EX + SIT and EX + BR (P < 0.05 relative to baseline), but afternoon time points were not significantly lower than baseline. The average MCAv over 8 h was higher in EX + SIT than SIT (P = 0.007) or EX + BR (P = 0.024). Uninterrupted sitting should be avoided, and moderate-intensity exercise should be encouraged for the daily maintenance of cerebral blood flow in older adults. The clinical implications of maintaining adequate cerebral blood flow include the delivery of vital oxygen and nutrients to the brain

Genetic Deletion of the Stromal Cell Marker CD248 (Endosialin) Protects against the Development of Renal Fibrosis

BACKGROUND: Tissue fibrosis and microvascular rarefaction are hallmarks of progressive renal disease. CD248 is a transmembrane glycoprotein expressed by key effector cells within the stroma of fibrotic kidneys including pericytes, myofibroblasts and stromal fibroblasts. In human disease, increased expression of CD248 by stromal cells predicts progression to end-stage renal failure. We therefore, hypothesized that the genetic deletion of the CD248 gene would protect against fibrosis following kidney injury. METHODS: Using the unilateral ureteral obstruction (UUO) model of renal fibrosis, we investigated the effect of genetic deletion of CD248 on post obstructive kidney fibrosis. RESULTS: CD248 null mice were protected from fibrosis and microvascular rarefaction following UUO. Although the precise mechanism is not known, this may to be due to a stabilizing effect of pericytes with less migration and differentiation of pericytes toward a myofibroblast phenotype in CD248(-/-) mice. CD248(-/-) fibroblasts also proliferated less and deposited less collagen in vitro. CONCLUSION: These studies suggest that CD248 stromal cells have a pathogenic role in renal fibrosis and that targeting CD248 is effective at inhibiting both microvascular rarefaction and renal fibrosis through modulation of pericyte and stromal cell function

Distinct Effects of Blood Flow and Temperature on Cutaneous Microvascular Adaptation

Aims: We performed two experiments to determine whether cutaneous microvascular adaptations in response to repeated core temperature elevation are mediated by increases in skin temperature, and/or, skin blood flow. Methods: Healthy subjects participated for 8-weeks in thrice-weekly bouts of 30mins lower limb heating (40°C). In Study 1, both forearms were “clamped” at basal skin temperature throughout each heating bout (n=9). Study 2 involved identical lower limb heating, with the forearms under ambient conditions (unclamped, n=10). In both studies, a cuff was inflated around one forearm during the heating bouts to assess the contribution of skin blood flow and temperature responses. We assessed forearm skin blood flow responses to both lower limb (systemic reflex) heating, and to local heating of the forearm skin, pre and post intervention. Results: Acutely, lower limb heating increased core temperature (Study 1: +0.63±0.15°C, Study 2: +0.69±0.19°C, P<0.001) and forearm skin blood flow (Study 1: 10±3 vs 125±44, Study 2: 16±9 vs 136±41 PU, P<0.001), with skin responses significantly attenuated in the cuffed forearm (P<0.01). Skin blood flow responses to local heating decreased in Study 1 (clamped forearms, week 0vs8: 1.46±0.52 vs 0.99±0.44 CVC, P<0.05), whereas increases occurred in Study 2 (unclamped; week 0vs8: 1.89±0.57 vs 2.27±0.52 CVC, P<0.05). Cuff placement abolished local adaptations in both studies. Conclusion: Our results indicate that repeated increases in skin blood flow and skin temperature result in increased skin flux responses to local heating, whereas repeated increases in skin blood flow in the absence of change in skin temperature induced the opposite response. Repeated increases in core temperature induce intrinsic microvascular changes, the nature of which are dependent upon both skin blood flow and skin temperature

Gait analysis in chronic heart failure: The calf as a locus of impaired walking capacity

Reduced walking capacity, a hallmark of chronic heart failure (CHF), is strongly correlated with hospitalization and morbidity. The aim of this work was to perform a detailed biomechanical gait analysis to better identify mechanisms underlying reduced walking capacity in CHF. Inverse dynamic analyses were conducted in CHF patients and age- and exercise level-matched control subjects on an instrumented treadmill at self-selected treadmill walking speeds and at speeds representing +20% and -20% of the subjects' preferred speed. Surprisingly, no difference in preferred speed was observed between groups, possibly explained by an optimization of the mechanical cost of transport in both groups (the mechanical cost to travel a given distance; J/kg/m). The majority of limb kinematics and kinetics were also similar between groups, with the exception of greater ankle dorsiflexion angles during stance in CHF. Nevertheless, over two times greater ankle plantarflexion work during stance and per distance traveled is required for a given triceps surae muscle volume in CHF patients. This, together with a greater reliance on the ankle compared to the hip to power walking in CHF patients, especially at faster speeds, may contribute to the earlier onset of fatigue in CHF patients. This observation also helps explain the high correlation between triceps surae muscle volume and exercise capacity that has previously been reported in CHF. Considering the key role played by the plantarflexors in powering walking and their association with exercise capacity, our findings strongly suggest that exercise-based rehabilitation in CHF should not omit the ankle muscle group