The Compton-Schwarzschild correspondence from extended de Broglie relations

The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point $(l_P,m_P)$, where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near $(l_P,m_P)$. It is unclear what physical interpretation can be given to quantum particles with energy $E \gg m_Pc^2$, since they correspond to wavelengths $\lambda \ll l_P$ or time periods $T \ll t_P$ in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schr{\" o}dinger equation and a modified expression for the Compton wavelength, which may be extended into the region $E \gg m_Pc^2$. For the proposed modification, we recover the expression for the Schwarzschild radius for $E \gg m_Pc^2$ and the usual Compton formula for $E \ll m_Pc^2$. The sign of the inequality obtained from the uncertainty principle reverses at $m \approx m_P$, so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the self-gravitation of the wave packet.Comment: 40 pages, 7 figures, 2 appendices. Published version, with additional minor typos corrected (v3

Accurate and efficient calculation of response times for groundwater flow

We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action time. Previous applications of the theory of mean action time to estimate the response time use the first two central moments of the probability density function associated with the transition from the initial condition, at $t=0$, to the steady state condition that arises in the long time limit, as $t \to \infty$. This previous approach leads to a computationally convenient estimation of the response time, but the accuracy can be poor. Here, we outline a powerful extension using the first $k$ raw moments, showing how to produce an extremely accurate estimate by making use of asymptotic properties of the cumulative distribution function. Results are validated using an existing laboratory-scale data set describing flow in a homogeneous porous medium. In addition, we demonstrate how the results also apply to flow in heterogeneous porous media. Overall, the new method is: (i) extremely accurate; and (ii) computationally inexpensive. In fact, the computational cost of the new method is orders of magnitude less than the computational effort required to study the response time by solving the transient flow equation. Furthermore, the approach provides a rigorous mathematical connection with the heuristic argument that the response time for flow in a homogeneous porous medium is proportional to $L^2/D$, where $L$ is a relevant length scale, and $D$ is the aquifer diffusivity. Here, we extend such heuristic arguments by providing a clear mathematical definition of the proportionality constant.Comment: 22 pages, 3 figures, accepted version of paper published in Journal of Hydrolog

New homogenization approaches for stochastic transport through heterogeneous media

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative jump coefficients can arise when transport operators are discretized on heterogeneous domains. Often this is dealt with through homogenization approximations by replacing the heterogeneous medium with an $\textit{effective}$ homogeneous medium. In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates. We derive closed form solutions for the $k$th moment of particle lifetime, carefully explaining how to deal with the internal interfaces between layers. These general tools allow us to derive simple formulae for the effective transport coefficients, leading to significant generalisations of previous homogenization approaches. Here, we find that different jump rates in the layers gives rise to a net bias, leading to a non-zero advection, for the entire homogenized system. Example calculations show that our generalized approach can lead to very different outcomes than traditional approaches, thereby having the potential to significantly affect simulation studies that use homogenization approximations.Comment: 9 pages, 2 figures, accepted version of paper published in The Journal of Chemical Physic

Investigating the local circulation of the southeast Cape Basin

Located off the west coast of southern Africa, the southeast Cape Basin is characterised by a unique combination of strong coastal upwelling and vigorous offshore mesoscale variability. The juxtaposition of offshore mesoscale variability and coastal upwelling results in a complex and dynamic environment. In this study a combination of in situ Acoustic Doppler Current Profiler (ADCP) data and satellite observations were used to identify, describe and characterise the features driving the local circulation within the southeast Cape Basin. The ADCP data was obtained from the South Atlantic MOC Basin-wide Array (SAMBA), which included four deep sea moorings located along ~34.5°S on the 1000, 2000, 3000 and 4500m isobaths respectively. There was a distinct difference in the circulation observed at the mooring located on the shelf edge (1000m) and the moorings further offshore (2000m, 3000m and 45000m). The offshore circulation, observed by the moorings located on the 2000, 3000, 4500m isobaths, were driven by large mesoscale eddies, both cyclonic and anticyclonic, originating at the Agulhas retroflection and within the Cape Basin itself. The mesoscale eddies induced high speed baroclinic transport events which impacted the upper water column to a depth of at least 400m. The in situ observations were used to show the precise characteristics of two cyclonic shelf eddies and one anticyclonic eddy through the upper water column (~50 to 500m). The analysis of these features was important as the physical characteristics of both the cyclonic shelf eddies and anticyclonic eddies through depth are not well known. Considering the short period of observations (18th September 2014 to 1st December 2015), the analysis was not used to assume the prevailing physical characteristics of cyclonic shelf eddies and anticyclonic eddies. Instead the analysis showed the potential for future long term studies to use the sustained in situ observations from the SAMBA mooring array and similar analysis to define the precise characteristics of mesoscale eddies through depth. This will greatly improve the understanding of how these features influence the interocean exchange between the Indian and Atlantic Oceans. The circulation at the shelf edge, observed by the mooring located on the 1000m isobath, was shown to be driven by a combination of offshore mesoscale eddies, the position of the upwelling front and warm filaments formed at the reflection of the Agulhas Current. Identifying the influence of both the offshore mesoscale eddies and coastal upwelling at the shelf edge showed connectivity between the upwelling system and the offshore mesoscale variability. An example of the connectivity between the offshore mesoscale variability and the upwelling front was identified and presented. A dipole formed by two mesoscale eddies was observed to induced cross shelf transport advecting productive shelf waters offshore. The in situ observations were used to calculate the amount water transported from the shelf to the open ocean during this cross shelf transport event. The filament representing the cross shelf transport event was calculated to have a total volume of ~2 x 10¹² m³ with a volume transport of ~1Sv suggesting the event would have had a substantial impact on the local biology. The detailed analysis and quantification of the cross shelf transport event aimed to improve the current understanding of how mesoscale features interact with the upwelling system. In situ observations of cross shelf transport are rare, therefore the quantification of the amount of transported in the cross shelf transport event can serve as a baseline for future studies attempting to assess the impact of comparable cross shelf transport events on the local biology

Computational Flow Dynamics Analysis of 5-holed Catalyst Geometries in Methane Steam Reforming

This project analyzed some new options for pellet geometry in SMR applications by using computational fluid dynamics software to model the behavior of three 5-holed geometries. This software analysis is necessary due to the high operating temperature of the reforming process which limits physical experimentation. Among the important qualities analyzed were pressure drop, heat transfer and methane conversion. The specific geometries studied were designated 5H-P, 5H-P-small, and 5H-Q. It was determined that while 5H-P is the best option of these three, it does not perform much more efficiently than the currently produced 4H-Q model. However, it was proposed that a modified 5H-Q pellet may result in better performance under reactor conditions

Urban Hostility: CPTED, Hostile Architecture, and the Erasure of Democratic Public Space

Free and open public space is essential to the health of urban living. In theory, it is purely neutral, acting as a social equalizer providing those of all backgrounds space to co-exist within the confines of the built environment. However, truly democratic public space has consistently been threatened and reduced in cities, affecting none more heavily than marginalized and impoverished populations. The creation of the Crime Prevention Through Environmental Design agenda gave birth to hostile architecture, a detrimental form of urban exclusionism. By using hostile design typologies, cities can render public spaces unusable to undesirable citizens, and subsequently erase images of poverty, social decay, and public disorder. The ways in which CPTED and hostile architecture have led to the alarming erasure of free public space will be addressed and the consequences this has upon marginalized populations will be portrayed

Working wetlands: classifying wetland potential for agriculture

Wetlands / Ecology / Natural resources / Social aspects / Case studies / Zanzibar / Tanzania / Zimbabwe / Swaziland

The effect of combined glutamate receptor blockade in the NTS on the hypoxic ventilatory response in awake rats differs from the effect of individual glutamate receptor blockade.

Ventilatory acclimatization to hypoxia (VAH) increases the hypoxic ventilatory response (HVR) and causes persistent hyperventilation when normoxia is restored, which is consistent with the occurrence of synaptic plasticity in acclimatized animals. Recently, we demonstrated that antagonism of individual glutamate receptor types (GluRs) within the nucleus tractus solitarii (NTS) modifies this plasticity and VAH (J. Physiol. 592(8):1839-1856); however, the effects of combined GluR antagonism remain unknown in awake rats. To evaluate this, we exposed rats to room air or chronic sustained hypobaric hypoxia (CSH, PiO2 = 70 Torr) for 7-9 days. On the experimental day, we microinjected artificial cerebrospinal fluid (ACSF: sham) and then a "cocktail" of the GluR antagonists MK-801 and DNQX into the NTS. The location of injection sites in the NTS was confirmed by glutamate injections on a day before the experiment and with histology following the experiment. Ventilation was measured in awake, unrestrained rats breathing normoxia or acute hypoxia (10% O2) in 15-min intervals using barometric pressure plethysmography. In control (CON) rats, acute hypoxia increased ventilation; NTS microinjections of GluR antagonists, but not ACSF, significantly decreased ventilation and breathing frequency in acute hypoxia but not normoxia (P < 0.05). CSH increased ventilation in hypoxia and acute normoxia. In CSH-conditioned rats, GluR antagonists in the NTS significantly decreased ventilation in normoxia and breathing frequency in hypoxia. A persistent HVR after combined GluR blockade in the NTS contrasts with the effect of individual GluR blockade and also with results in anesthetized rats. Our findings support the hypotheses that GluRs in the NTS contribute to, but cannot completely explain, VAH in awake rats

Maximizing Return: An Evaluation of the Walton Family Foundation’s Approach to Investing in New Charter Schools

The Walton Family Foundation’s social-impact goals include reform of the American K-12 education system by increasing the number of highquality schools available to low-income students. One of the foundation’s signature strategies toward this end is to support charter schools. This article presents the findings of a study that suggests the foundation’s investment approaches to charter school startups have been successful in supporting the creation of high-quality seats for low-income students. Specifically, the foundation has invested in charter schools where test-score performance has shown greater improvements than at local district schools and charter schools that have not received foundation funding. These approaches could be incorporated by other foundations interested in investing in the creation of new schools but unsure how best to maximize the likelihood that those schools will be successful