A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions

A major challenge in studying coupled groundwater and surface-water interactions arises from the considerable difference in the response time scales of groundwater and surface-water systems affected by external forcings. Although coupled models representing the interaction of groundwater and surface-water systems have been studied for over a century, most have focused on groundwater quantity or quality issues rather than response time. In this study, we present an analytical framework, based on the concept of mean action time (MAT), to estimate the time scale required for groundwater systems to respond to changes in surface-water conditions. MAT can be used to estimate the transient response time scale by analyzing the governing mathematical model. This framework does not require any form of transient solution (either numerical or analytical) to the governing equation, yet it provides a closed form mathematical relationship for the response time as a function of the aquifer geometry, boundary conditions, and flow parameters. Our analysis indicates that aquifer systems have three fundamental time scales: (i) a time scale that depends on the intrinsic properties of the aquifer; (ii) a time scale that depends on the intrinsic properties of the boundary condition, and; (iii) a time scale that depends on the properties of the entire system. We discuss two practical scenarios where MAT estimates provide useful insights and we test the MAT predictions using new laboratory-scale experimental data sets.

Multifractal analyses of daily rainfall time series in Pearl River basin of China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter HH from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h(2)h(2) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K(2)K(2) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

Relationship over time between psychological distress and physical activity in colorectal cancer survivors

Purpose Increased physical activity in colorectal cancer patients is related to improved recurrence free and overall survival. Psychological distress after cancer may place patients at risk of reduced physical activity; but paradoxically also act as a motivator for positive lifestyle change. The relationship between psychological distress and physical activity after cancer over time has not been described. Methods A prospective survey of 1966 (57% response) colorectal cancer survivors assessed the psychological distress variables of anxiety, depression, somatisation, cancer threat appraisal as predictors of physical activity five, 12, 24 and 36 months post-diagnosis 978 respondents had valid data for all time points. Results Higher somatisation was associated with greater physical inactivity (Relative risk ratio (RRR) =1.12; 95% CI=[1.1, 1.2]) and insufficient physical activity (RRR=1.05; [0.90, 1.0]). Respondents with a more positive appraisal of their cancer were significantly (p=0.031) less likely to be inactive (RRR=0.95; [0.90, 1.0]) or insufficiently active (RRR=0.96). Fatigued and obese respondents and current smokers were more inactive. Respondents whose somatisation increased between two time periods were less likely to increase their physical activity over the same period (p<0.001). Respondents with higher anxiety at one time period were less likely to have increased their activity at the next assessment (p=0.004). There was no association between depression and physical activity. Conclusions Cancer survivors who experience somatisation and anxiety are at greater risk of physical inactivity. The lack of a clear relationship between higher psychological distress and increasing physical activity argues against distress as a motivator to exercise in these patients.

Do strategy choices matter for nascent firms? A study on effectuation and causation impacts on new ventures outcomes

Principal Topic : Nascent entrepreneurship has drawn the attention of scholars in the last few years (Davidsson, 2006, Wagner, 2004). However, most studies have asked why firms are created focussing on questions such as what are the characteristics (Delmar and Davidsson, 2000) and motivations (Carter, Gartner, Shaver & Reynolds, 2004) of nascent entrepreneurs, or what are the success factors in venture creation (Davidsson & Honig; 2003; Delmar and Shane, 2004). In contrast, the question of how companies emerge is still in its infancy. On a theoretical side, effectuation, developed by Sarasvathy (2001) offers one view of the strategies that may be at work during the venture creation process. Causation, the theorized inverse to effectuation, may be described as a rational reasoning method to create a company. After a comprehensive market analysis to discover opportunities, the entrepreneur will select the alternative with the higher expected return and implement it through the use of a business plan. In contrast, effectuation suggests that the future entrepreneur will develop her new venture in a more iterative way by selecting possibilities through flexibility and interaction with the market, affordability of loss of resources and time invested, development of pre-commitments and alliances from stakeholders. Another contrasting point is that causation is ''goal driven'' while an effectual approach is ''mean driven'' (Sarasvathy, 2001) One of the predictions of effectuation theory is effectuation is more likely to be used by entrepreneurs early in the venture creation process (Sarasvathy, 2001). However, this temporal aspect and the impact of the effectuation strategy on the venture outcomes has so far not been systematically and empirically tested on large samples. The reason behind this research gap is twofold. Firstly, few studies collect longitudinal data on emerging ventures at an early enough stage of development to avoid severe survivor bias. Second, the studies that collect such data have not included validated measures of effectuation. The research we are conducting attempts to partially fill this gap by combining an empirical investigation on a large sample of nascent and young firms with the effectuation/causation continuum as a basis (Sarasvathy, 2001). The objectives are to understand the strategies used by the firms during the creation process and measure their impacts on the firm outcomes. Methodology/Key Propositions : This study draws its data from the first wave of the CAUSEE project where 28,383 Australian households were randomly contacted by phone using a specific methodology to capture emerging firms (Davidsson, Steffens, Gordon, Reynolds, 2008). This screening led to the identification of 594 nascent ventures (i.e., firms that are not operating yet) and 514 young firms (i.e., firms that have started operating from 2004) that were willing to participate in the study. Comprehensive phone interviews were conducted with these 1108 ventures. In a likewise comprehensive follow-up 12 months later, 80% of the eligible cases completed the interview. The questionnaire contains specific sections designed to distinguish effectual and causal processes, innovation, gestation activities, business idea changes and ventures outcomes. The effectuation questions are based on the components of effectuation strategy as described by Sarasvathy (2001) namely: flexibility, affordable loss and pre-commitment from stakeholders. Results from two rounds of pre-testing informed the design of the instrument included in the main survey. The first two waves of data have will be used to test and compare the use of effectuation in the venture creation process. To increase the robustness of the results, temporal use of effectuation will be tested both directly and indirectly. 1. By comparing the use of effectuation in nascent and young firms from wave 1 to 2, we will be able to find out how effectuation is affected by time over a 12-month duration and if the stage of venture development has an impact on its use. 2. By comparing nascent ventures early in the creation process versus nascent ventures late in the creation process. Early versus late can be determined with the help of time-stamped gestation activity questions included in the survey. This will help us to determine the change on a small time scale during the creation phase of the venture. 3. By comparing nascent firms to young (already operational) firms. 4. By comparing young firms becoming operational in 2006 with those first becoming operational in 2004. Results and Implications : Wave 1 and 2 data have been completed and wave 2 is currently being checked and 'cleaned'. Analysis work will commence in September, 2009. This paper is expected to contribute to the body of knowledge on effectuation by measuring quantitatively its use and impact on nascent and young firms activities at different stages of their development. In addition, this study will also increase the understanding of the venture creation process by comparing over time nascent and young firms from a large sample of randomly selected ventures. We acknowledge the results from this study will be preliminary and will have to be interpreted with caution as the changes identified may be due to several factors and may not only be attributed to the use/not use of effectuation. Meanwhile, we believe that this study is important to the field of entrepreneurship as it provides some much needed insights on the processes used by nascent and young firms during their creation and early operating stages.

Driving performance impairments due to hypovigilance on monotonous roads

Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads.

Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions

In this study, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden and linear changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The instantaneous and non-instantaneous (ramp) heating boundary condition is applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

One-year delayed effect of fog on malaria transmission : a time-series analysis in the rain forest area of Mengla County, south-west China

Background: Malaria is a major public health burden in the tropics with the potential to significantly increase in response to climate change. Analyses of data from the recent past can elucidate how short-term variations in weather factors affect malaria transmission. This study explored the impact of climate variability on the transmission of malaria in the tropical rain forest area of Mengla County, south-west China. Methods: Ecological time-series analysis was performed on data collected between 1971 and 1999. Auto-regressive integrated moving average (ARIMA) models were used to evaluate the relationship between weather factors and malaria incidence. Results: At the time scale of months, the predictors for malaria incidence included: minimum temperature, maximum temperature, and fog day frequency. The effect of minimum temperature on malaria incidence was greater in the cool months than in the hot months. The fog day frequency in October had a positive effect on malaria incidence in May of the following year. At the time scale of years, the annual fog day frequency was the only weather predictor of the annual incidence of malaria. Conclusion: Fog day frequency was for the first time found to be a predictor of malaria incidence in a rain forest area. The one-year delayed effect of fog on malaria transmission may involve providing water input and maintaining aquatic breeding sites for mosquitoes in vulnerable times when there is little rainfall in the 6-month dry seasons. These findings should be considered in the prediction of future patterns of malaria for similar tropical rain forest areas worldwide.

Nitrous oxide emissions from subtropical horticultural soils : a time series analysis

Time series regression models were used to examine the influence of environmental factors (soil water content and soil temperature) on the emissions of nitrous oxide (N2O) from subtropical soils, by taking into account temporal lagged environmental factors, autoregressive processes, and seasonality for three horticultural crops in a subtropical region of Australia. Fluxes of N2O, soil water content, and soil temperature were determined simultaneously on a weekly basis over a 12-month period in South East Queensland. Annual N2O emissions for soils under mango, pineapple, and custard apple were 1590, 1156, and 2038 g N2O-N/ha, respectively, with most emissions attributed to nitrification. The N2O-N emitted from the pineapple and custard apple crops was equivalent to 0.26 and 2.22%, respectively, of the applied mineral N. The change in soil water content was the key variable for describing N2O emissions at the weekly time-scale, with soil temperature at a lag of 1 month having a significant influence on average N2O emissions (averaged) at the monthly time-scale across the three crops. After accounting for soil temperature and soil water content, both the weekly and monthly time series regression models exhibited significant autocorrelation at lags of 1–2 weeks and 1–2 months, and significant seasonality for weekly N2O emissions for mango crop and for monthly N2O emissions for mango and custard apple crops in this location over this time-frame. Time series regression models can explain a higher percentage of the temporal variation of N2O emission compared with simple regression models using soil temperature and soil water content as drivers. Taking into account seasonal variability and temporal persistence in N2O emissions associated with soil water content and soil temperature may lead to a reduction in the uncertainty surrounding estimates of N2O emissions based on limited sampling effort.

Pore size distribution and accessible pore size distribution in bituminous coals

The porosity and pore size distribution of coals determine many of their properties, from gas release to their behavior on carbonization, and yet most methods of determining pore size distribution can only examine a restricted size range. Even then, only accessible pores can be investigated with these methods. Small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) are increasingly used to characterize the size distribution of all of the pores non-destructively. Here we have used USANS/SANS to examine 24 well-characterized bituminous and subbituminous coals: three from the eastern US, two from Poland, one from New Zealand and the rest from the Sydney and Bowen Basins in Eastern Australia, and determined the relationships of the scattering intensity corresponding to different pore sizes with other coal properties. The range of pore radii examinable with these techniques is 2.5nm to 7μm. We confirm that there is a wide range of pore sizes in coal. The pore size distribution was found to be strongly affected by both rank and type (expressed as either hydrogen or vitrinite content) in the size range 250nm to 7μm and 5 to 10nm, but weakly in intermediate regions. The results suggest that different mechanisms control coal porosity on different scales. Contrast-matching USANS and SANS were also used to determine the size distribution of the fraction of the pores in these coals that are inaccessible to deuterated methane, CD4, at ambient temperature. In some coals most of the small (~10nm) pores were found to be inaccessible to CD4 on the time scale of the measurement (~30min–16h). This inaccessibility suggests that in these coals a considerable fraction of inherent methane may be trapped for extended periods of time, thus reducing the effectiveness of methane release from (or sorption by) these coals. Although the number of small pores was less in higher rank coals, the fraction of total pores that was inaccessible was not rank dependent. In the Australian coals, at the 10nm to 50nm size scales the pores in inertinites appeared to be completely accessible to CD4, whereas the pores in the vitrinite were about 75% inaccessible. Unlike the results for total porosity that showed no regional effects on relationships between porosity and coal properties, clear regional differences in the relationships between fraction of closed porosity and coal properties were found. The 10 to 50nm-sized pores of inertinites of the US and Polish coals examined appeared less accessible to methane than those of the inertinites of Australian coals. This difference in pore accessibility in inertinites may explain why empirical relationships between fluidity and coking properties developed using Carboniferous coals do not apply to Australian coals.

First full-scale trials of pebble matrix filtration

Protecting slow sand filters from high turbidity waters by pre-treatment using Pebble Matrix Filtration (PMF) has been studied in the laboratory at University College London followed by pilot field trials in Papua New Guinea and Serbia. Subsequently, the construction of two full-scale PMF units, one out of concrete (4.8m x4.8m x 3.0m high) and the other using pre-cast Ferro-cement panels (900mm x 1600mm x 20mm thick) with an effective diameter of 4.7m and 3m height, and the combined effective plan area of 40 m2 was completed to protect an existing Slow Sand Filter system at the National Water Supply Drainage Board (NWSDB) in Sri Lanka. Although the plant was completed in April 2008 due to some major repairs to address some leaks and other construction defects in both filters, monitoring was intermittent until November 2008. The results on the plant performance are presented here along with some of the construction problems encountered during the project.

How much information can be obtained from tracking the position of the leading edge in a scratch assay?

Moving cell fronts are an essential feature of wound healing, development and disease. The rate at which a cell front moves is driven, in part, by the cell motility, quantified in terms of the cell diffusivity $D$, and the cell proliferation rate �$\lambda$. Scratch assays are a commonly-reported procedure used to investigate the motion of cell fronts where an initial cell monolayer is scratched and the motion of the front is monitored over a short period of time, often less than 24 hours. The simplest way of quantifying a scratch assay is to monitor the progression of the leading edge. Leading edge data is very convenient since, unlike other methods, it is nondestructive and does not require labeling, tracking or counting individual cells amongst the population. In this work we study short time leading edge data in a scratch assay using a discrete mathematical model and automated image analysis with the aim of investigating whether such data allows us to reliably identify $D$ and $\lambda$�. Using a naıve calibration approach where we simply scan the relevant region of the ($D$;$\lambda$�) parameter space, we show that there are many choices of $D$ and $\lambda$� for which our model produces indistinguishable short time leading edge data. Therefore, without due care, it is impossible to estimate $D$ and $\lambda$� from this kind of data. To address this, we present a modified approach accounting for the fact that cell motility occurs over a much shorter time scale than proliferation. Using this information we divide the duration of the experiment into two periods, and we estimate $D$ using data from the first period, while we estimate �$\lambda$ using data from the second period. We confirm the accuracy of our approach using in silico data and a new set of in vitro data, which shows that our method recovers estimates of $D$ and $\lamdba$� that are consistent with previously-reported values except that that our approach is fast, inexpensive, nondestructive and avoids the need for cell labeling and cell counting.

Depression and belongingness in general and workplace contexts : a cross-lagged longitudinal investigation

Belongingness has been linked to depression. Prior studies have been cross-sectional with few addressing distinct belongingness contexts. This study used structural equation modelling to investigate cross-lagged longitudinal relationships between general belonging, workplace belonging and depressive symptoms in a community sample of 221 working adults measured at two time points three months apart. Measures were: Sense of Belonging Instrument-Psychological (SOBI-P); Psychological Sense of Organizational Membership (PSOM); Depression Anxiety Stress Scales (DASS-21); Kessler Psychological Distress Scale (K10). General belonging was predicted more strongly by depressive symptoms than by baseline general belonging, suggesting that depressive symptoms not only linger but also influence future belongingness cognitions. Neither general nor workplace belonging longitudinally predicted depressive symptoms, however cross-sectional correlations were substantial. The concurrent path between general belongingness and depressive symptoms was strong. Results are consistent with daily process studies suggesting that reduced belongingness precipitates a rapid increase in depressive symptoms which influence longer term belongingness cognitions. Congruent with interpersonal descriptions of depression such as the social-cognitive interpersonal process model, results further suggest that belongingness cognitions are the proximal antecedent of a depressive response. Practitioners should monitor both a general sense of belonging as well as perceived relational value cues in specific contexts.

Development and application of Palygorskite porous ceramsite in a biological aerated filter (BAF)

Novel filter Palygorskite porous ceramsite (PC) was prepared using Palygorskite clay, poreforming material sawdust, and sodium silicate with a mass ratio of 10:2:1 after sintering at 700°C for 180 min. PC was characterized with X-ray diffraction, X-ray fluorescence, scanning electron microscopy, elemental, and porosimetry. PC had a total porosity of 67% and specific surface area of 61 m2/g. In order to assess the usefulness of PC as a medium for biological aerated filters (BAF), PC and (commercially available ceramsite) CAC were used to treat wastewater city in two laboratory-scale upflow BAFs. The results showed that the reactor containing PC was more efficient than the reactor containing CAC in terms of total organic carbon (TOC), ammonia nitrogen (NH3-N), and the removal of total nitrogen (TN) and phosphorus (P). This system was found to be more efficient at water temperatures ranging from 20 to 26°C, an air–water (A/W) ratio of 3:1, dissolved oxygen concentration >4.00 mg/L, and hydraulic retention time (HRT) ranging from 0.5 to 7 h. The interconnected porous structure produced for PC was suitable for microbial growth, and primarily protozoan and metazoan organisms were found in the biofilm. Microorganism growth also showed that, under the same submerged culture conditions, the biological mass in PC was significantly higher than in CAC (34.1 and 2.2 mg TN/g, respectively). In this way, PC media can be considered suitable for the use as a medium in novel biological aerated filters for the simultaneous removal of nitrogen and phosphorus.