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

COLONIZATION OF NORTHERN LOUISIANA BY THE MEDITERRANEAN GECKO, HEMIDACTYLUS TURCICUS

The Mediterranean Gecko, Hemidactylus turcicus, is known to have colonized nearly every state in the southern United States. In Louisiana, the Mediterranean Gecko has been documented in many of the southern parishes, but records for the northern portion of the state are limited. We sampled northern Louisiana parishes to document the presence of the Mediterranean Gecko. We sampled a total of 21 parishes in northern Louisiana and found geckos in 17 of those parishes, 16 of which represent new distribution records for the species. This indicates a significant range expansion of this introduced species throughout northern Louisiana. Geckos were found across a temperature range of 14.0–28.0°C and had a strong association with buildings. The species’ affinity for anthropogenic association and the continual nature of anthropogenic expansion facilitate the high vagility of this species. The result is a successful colonization throughout much of Louisiana and likely continued range expansion throughout the southern United States

Working wetlands: classifying wetland potential for agriculture

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

High-Resolution Near Infrared Spectroscopy of HD 100546: II. Analysis of variable rovibrational CO emission lines

We present observations of rovibrational CO in HD 100546 from four epochs spanning January 2003 through December 2010. We show that the equivalent widths of the CO lines vary during this time period with the v=1-0 CO lines brightening more than the UV fluoresced lines from the higher vibrational states. While the spectroastrometric signal of the hot band lines remains constant during this period, the spectroastrometric signal of the v=1--0 lines varies substantially. At all epochs, the spectroastrometric signals of the UV fluoresced lines are consistent with the signal one would expect from gas in an axisymmetric disk. In 2003, the spectroastrometric signal of the v=1-0 P26 line was symmetric and consistent with emission from an axisymmetric disk. However, in 2006, there was no spatial offset of the signal detected on the red side of the profile, and in 2010, the spectroastrometric offset was yet more strongly reduced toward zero velocity. A model is presented that can explain the evolution of the equivalent width of the v=1-0 P26 line and its spectroastrometric signal by adding to the system a compact source of CO emission that orbits the star near the inner edge of the disk. We hypothesize that such emission may arise from a circumplanetary disk orbiting a gas giant planet near the inner edge of the circumstellar disk. We discuss how this idea can be tested observationally and be distinguished from an alternative interpretation of random fluctuations in the disk emission.Comment: 18 pages, 10 figure

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