Critical time scales for advection–diffusion–reaction processes

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and coworkers in 2010–2011 to give a finite measure of the time required for the transient solution of a reaction–diffusion equation to approach the steady–state solution (Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb in 1991 (IMA J Appl Math. 47, 193 (1991)). Although McNabb’s initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one–dimensional linear advection–diffusion–reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform–to-uniform transitions; these results provide a practical interpretation for MAT, by directly linking the stochastic microscopic processes to a meaningful macroscopic timescale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using the MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Moments of action provide insight into critical times for advection–diffusion–reaction processes

In 2010 Berezhkovskii and coworkers introduced the concept of local accumulation time (LAT) as a finite measure of the time required for the transient solution of a reaction diffusion equation to effectively reach steady state(Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Berezhkovskii’s approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb (IMA J Appl Math. 47, 193 (1991)). Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time; the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one–dimensional linear advection–diffusion–reaction partial differential equation(PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.

Public realm and transport, international best practice case studies and opportunities for Brisbane

This report was prepared for Lat 27 Pty Ltd for the purpose of conducting a City Centre Public Realm and Active Transport Study for Urban Renewal Brisbane, Brisbane City Council. In this review, we highlight some key learnings and recommendations from innovative projects across the globe to inform public realm design and help facilitate active transport in subtropical Brisbane. Traditionally, Australian cities have been have been based on northern European models. This report is informed by the view that planners and urban designers must look beyond that paradigm to redefine and re-conceptualise our city in a different way, one that values our unique local identity and climate. In re-designing Brisbane’s public realm, therefore, design interventions and responses must celebrate our unique identity and outdoor lifestyle and address the subtropical climate's reality of life in warm humid summers and cool dry winters. The current period of rapid urban change, and the imperative to adapt to climate change, together offer an opportunity to prioritise and integrate design features that provide shade and shelter from sun and summer rain, open and permeable urban environments that facilitate cooling air movement, and connections to water and nature, so that the urban built form co-exists within an inviting, functional and memorable natural landscape. To inform this transformation, this review provides insight into international experiences and best practices. To date, although there is much practice-based knowledge, academic studies outlining learnings and recommendations from case studies (especially in a subtropical context) remain rare. Thus, a range of sources (industry reports, websites, journal articles and books) have been utilised.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Targeting amino acid transport in metastatic castration-resistant prostate cancer : effects on cell cycle, cell growth, and tumor development

Background L-type amino acid transporters (LATs) uptake neutral amino acids including L-leucine into cells, stimulating mammalian target of rapamycin complex 1 signaling and protein synthesis. LAT1 and LAT3 are overexpressed at different stages of prostate cancer, and they are responsible for increasing nutrients and stimulating cell growth. Methods We examined LAT3 protein expression in human prostate cancer tissue microarrays. LAT function was inhibited using a leucine analog (BCH) in androgen-dependent and -independent environments, with gene expression analyzed by microarray. A PC-3 xenograft mouse model was used to study the effects of inhibiting LAT1 and LAT3 expression. Results were analyzed with the Mann-Whitney U or Fisher exact tests. All statistical tests were two-sided. Results LAT3 protein was expressed at all stages of prostate cancer, with a statistically significant decrease in expression after 4–7 months of neoadjuvant hormone therapy (4–7 month mean = 1.571; 95% confidence interval = 1.155 to 1.987 vs 0 month = 2.098; 95% confidence interval = 1.962 to 2.235; P = .0187). Inhibition of LAT function led to activating transcription factor 4–mediated upregulation of amino acid transporters including ASCT1, ASCT2, and 4F2hc, all of which were also regulated via the androgen receptor. LAT inhibition suppressed M-phase cell cycle genes regulated by E2F family transcription factors including critical castration-resistant prostate cancer regulatory genes UBE2C, CDC20, and CDK1. In silico analysis of BCH-downregulated genes showed that 90.9% are statistically significantly upregulated in metastatic castration-resistant prostate cancer. Finally, LAT1 or LAT3 knockdown in xenografts inhibited tumor growth, cell cycle progression, and spontaneous metastasis in vivo. Conclusion Inhibition of LAT transporters may provide a novel therapeutic target in metastatic castration-resistant prostate cancer, via suppression of mammalian target of rapamycin complex 1 activity and M-phase cell cycle genes.

Mid-Holocene sea-level and coral reef demise : U-Th dating of subfossil corals in Moreton Bay, Australia

It is increasingly apparent that sea-level data (e.g. microfossil transfer functions, dated coral microatolls and direct observations from satellite and tidal gauges) vary temporally and spatially at regional to local scales, thus limiting our ability to model future sea-level rise for many regions. Understanding sealevel response at ‘far-field’ locations at regional scales is fundamental for formulating more relevant sea-level rise susceptibility models within these regions under future global change projections. Fossil corals and reefs in particular are valuable tools for reconstructing past sea levels and possible environmental phase shifts beyond the temporal constraints of instrumental records. This study used abundant surface geochronological data based on in situ subfossil corals and precise elevation surveys to determine previous sea level in Moreton Bay, eastern Australia, a far-field site. A total of 64 U-Th dates show that relative sea level was at least 1.1 m above modern lowest astronomical tide (LAT) from at least ˜6600 cal. yr BP. Furthermore, a rapid synchronous demise in coral reef growth occurred in Moreton Bay ˜5800 cal. yr BP, coinciding with reported reef hiatus periods in other areas around the Indo-Pacific region. Evaluating past reef growth patterns and phases allows for a better interpretation of anthropogenic forcing versus natural environmental/climatic cycles that effect reef formation and demise at all scales and may allow better prediction of reef response to future global change.