An approach for identifying the limit states of resilience of a water supply system

This paper presents an approach for identifying the limit states of resilience in a water supply system when influenced by different types of pressure (disturbing) forces. Understanding of systemic resilience facilitates identification of the trigger points for early managerial action to avoid further loss of ability to provide satisfactory service availability when the ability to supply water is under pressure. The approach proposed here is to illustrate the usefulness of a surrogate measure of resilience depicted in a three dimensional space encompassing independent pressure factors. That enables visualisation of the transition of the system-state (resilience) between high to low resilience regions and acts as an early warning trigger for decision-making. The necessity of a surrogate measure arises as a means of linking resilience to the identified pressures as resilience cannot be measured directly. The basis for identifying the resilience surrogate and exploring the interconnected relationships within the complete system, is derived from a meta-system model consisting of three nested sub-systems representing the water catchment and reservoir; treatment plant; and the distribution system and end-users. This approach can be used as a framework for assessing levels of resilience in different infrastructure systems by identifying a surrogate measure and its relationship to relevant pressures acting on the system.

How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

Laboratory measurement of hydraulic conductivity functions of two unsaturated sandy soils during drying and wetting processes

The importance of applying unsaturated soil mechanics to geotechnical engineering design has been well understood. However, the consumption of time and the necessity for a specific laboratory testing apparatus when measuring unsaturated soil properties have limited the application of unsaturated soil mechanics theories in practice. Although methods for predicting unsaturated soil properties have been developed, the verification of these methods for a wide range of soil types is required in order to increase the confidence of practicing engineers in using these methods. In this study, a new permeameter was developed to measure the hydraulic conductivity of unsaturated soils using the steady-state method and directly measured suction (negative pore-water pressure) values. The apparatus is instrumented with two tensiometers for the direct measurement of suction during the tests. The apparatus can be used to obtain the hydraulic conductivity function of sandy soil over a low suction range (0-10 kPa). Firstly, the repeatability of the unsaturated hydraulic conductivity measurement, using the new permeameter, was verified by conducting tests on two identical sandy soil specimens and obtaining similar results. The hydraulic conductivity functions of the two sandy soils were then measured during the drying and wetting processes of the soils. A significant hysteresis was observed when the hydraulic conductivity was plotted against the suction. However, the hysteresis effects were not apparent when the conductivity was plotted against the volumetric water content. Furthermore, the measured unsaturated hydraulic conductivity functions were compared with predictions using three different predictive methods that are widely incorporated into numerical software. The results suggest that these predictive methods are capable of capturing the measured behavior with reasonable agreement.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation, and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Dynamics of a dilute sheared inelastic fluid. II. The effect of correlations

The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in epsilon=(1-e)(1/2) is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit epsilon -> 0. This implies that the most dominant correlation effects are due to the two-particle correlations.

The limit to wheat water-use efficiency in eastern Australia. II. Influence of rainfall patterns

We investigated the influence of rainfall patterns on the water-use efficiency of wheat in a transect between Horsham (36°S) and Emerald (23°S) in eastern Australia. Water-use efficiency was defined in terms of biomass and transpiration, WUEB/T, and grain yield and evapotranspiration, WUEY/ET. Our working hypothesis is that latitudinal trends in WUEY/ET of water-limited crops are the complex result of southward increasing WUEB/T and soil evaporation, and season-dependent trends in harvest index. Our approach included: (a) analysis of long-term records to establish latitudinal gradients of amount, seasonality, and size-structure of rainfall; and (b) modelling wheat development, growth, yield, water budget components, and derived variables including WUEB/T and WUEY/ET. Annual median rainfall declined from around 600 mm in northern locations to 380 mm in the south. Median seasonal rain (from sowing to harvest) doubled between Emerald and Horsham, whereas median off-season rainfall (harvest to sowing) ranged from 460 mm at Emerald to 156 mm at Horsham. The contribution of small events (≤ 5 mm) to seasonal rainfall was negligible at Emerald (median 15 mm) and substantial at Horsham (105 mm). Power law coefficients (τ), i.e. the slopes of the regression between size and number of events in a log-log scale, captured the latitudinal gradient characterised by an increasing dominance of small events from north to south during the growing season. Median modelled WUEB/T increased from 46 kg/ha.mm at Emerald to 73 kg/ha.mm at Horsham, in response to decreasing atmospheric demand. Median modelled soil evaporation during the growing season increased from 70 mm at Emerald to 172 mm at Horsham. This was explained by the size-structure of rainfall characterised with parameter τ, rather than by the total amount of rainfall. Median modelled harvest index ranged from 0.25 to 0.34 across locations, and had a season-dependent latitudinal pattern, i.e. it was greater in northern locations in dry seasons in association with wetter soil profiles at sowing. There was a season-dependent latitudinal pattern in modelled WUEY/ET. In drier seasons, high soil evaporation driven by a very strong dominance of small events, and lower harvest index override the putative advantage of low atmospheric demand and associated higher WUEB/T in southern locations, hence the significant southwards decrease in WUEY/ET. In wetter seasons, when large events contribute a significant proportion of seasonal rain, higher WUEB/T in southern locations may translate into high WUEY/ET. Linear boundary functions (French-Schultz type models) accounting for latitudinal gradients in its parameters, slope, and x-intercept, were fitted to scatter-plots of modelled yield v. evapotranspiration. The x-intercept of the model is re-interpreted in terms of rainfall size structure, and the slope or efficiency multiplier is described in terms of the radiation, temperature, and air humidity properties of the environment. Implications for crop management and breeding are discussed.

Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

Threshold photoproduction of charged pions on14N

Pion photoproduction processes14Ngs(gamma, pgr +)14C and14Ngs(gamma, pgr –)14O have been studied in the threshold region. These processes provide an excellent tool to study the corrections to soft pion theorems and Kroll-Ruderman limit as applied to nuclear processes. The agreement with the available experimental data for these processes is better with the empirical wave functions while the shell-model wave functions predict a much higher value. Detailed experimental studies of these reactions at threshold, it is shown, are expected to lead to a better understanding of the shell-model inputs and radial distributions in the 1p state. We thank Dr. S.C.K. Nair for a helpful discussion during the initial stages of this work. One of us (MVN) thanks Dr. J.M. Laget for sending some unpublished data on pion photoproduction. He is also thankful to Dr. J. Pasupathy and Dr. R. Rajaraman for their interest and encouragement.

Computational studies on new chemical species in the gas-phase and the solid-state.

There is intense activity in the area of theoretical chemistry of gold. It is now possible to predict new molecular species, and more recently, solids by combining relativistic methodology with isoelectronic thinking. In this thesis we predict a series of solid sheet-type crystals for Group-11 cyanides, MCN (M=Cu, Ag, Au), and Group-2 and 12 carbides MC2 (M=Be-Ba, Zn-Hg). The idea of sheets is then extended to nanostrips which can be bent to nanorings. The bending energies and deformation frequencies can be systematized by treating these molecules as an elastic bodies. In these species Au atoms act as an 'intermolecular glue'. Further suggested molecular species are the new uncongested aurocarbons, and the neutral Au_nHg_m clusters. Many of the suggested species are expected to be stabilized by aurophilic interactions. We also estimate the MP2 basis-set limit of the aurophilicity for the model compounds [ClAuPH_3]_2 and [P(AuPH_3)_4]^+. Beside investigating the size of the basis-set applied, our research confirms that the 19-VE TZVP+2f level, used a decade ago, already produced 74 % of the present aurophilic attraction energy for the [ClAuPH_3]_2 dimer. Likewise we verify the preferred C4v structure for the [P(AuPH_3)_4]^+ cation at the MP2 level. We also perform the first calculation on model aurophilic systems using the SCS-MP2 method and compare the results to high-accuracy CCSD(T) ones. The recently obtained high-resolution microwave spectra on MCN molecules (M=Cu, Ag, Au) provide an excellent testing ground for quantum chemistry. MP2 or CCSD(T) calculations, correlating all 19 valence electrons of Au and including BSSE and SO corrections, are able to give bond lengths to 0.6 pm, or better. Our calculated vibrational frequencies are expected to be better than the currently available experimental estimates. Qualitative evidence for multiple Au-C bonding in triatomic AuCN is also found.

Regional Integration and the State : The Changing Nature of Sovereignty in Southern Africa and Europe

The study explores the role of the state in regional integration processes. The question is approached through theoretical discussion and two case-studies - SADC (Southern African Development Community) and the EU. The main research question of the study is, what are the possibilities and problems of the integration process in Southern Africa and how do they differ from the possibilities and problems of the integration process in Europe. The undelrying question of the study is why do states decide to participate in an integration process where they have to limit their sovereignty. Review of the theoretical discussion of the integration studies shows that the integration process is affected by several factors on different levels of the international system. But the state plays a central role in integration processes - integration processes are inititated and carried on by the participatig states. The European integration process shows that the interests of the state can change over time. At the beginning of the integration process, the objective was to strengthen participating states. Later EU member states have decided that it is in their interest to deepen the process even if it has meant limitation of their sovereignty. The determinant factor has been that the member states have considered it to be in their interst to deepen the process. In Southern Africa the integration process is only at the beginning. SADC aims to establish a free trade area by 2008. The biggest challenge is how to implement the integration process so that it benefits all member states in a region that is economically dominated by South Africa. In practice this can be achieved through establishment of corrective mechanisms, which ensure equitable distribution of benefits. This would require deeper integration and South Africa to adapt responsibility towards its regional partners. African integration processes in general have not been as successful as for example the EU. African states have been reluctant to limit their sovereignty in favour of regional organisations.This can be explained by the differences between European and African states. The EU member states have been democracies while African states have been characterised by concentration of power in the executive branch. Furthermore the political systems in Africa have been characterised by vertical clientelist reltionships. As a result it has not been in the interest of the political elite to limit the state sovereignty in favour of regional organisations. In recent years SADC has been relatively succesful in its integration process and reforms, but a lot remains to be done before the implementation of the free trade area can be succesful. The institutional structure and treaties of SADC differ from the structures of the EU. Member states are the main actors of the integration processes. Their differences are reflected in the process and produce different kinds of integration in different parts of the world.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

ORP1L, a new Rab7 effector and regulator of late endosome functions

Oxysterol binding protein (OSBP) homologues have been found in eukaryotic organisms ranging from yeast to humans. These evolutionary conserved proteins have in common the presence of an OSBP-related domain (ORD) which contains the fully conserved EQVSHHPP sequence motif. The ORD forms a barrel structure that binds sterols in its interior. Other domains and sequence elements found in OSBP-homologues include pleckstrin homology domains, ankyrin repeats and two phenylalanines in an acidic tract (FFAT) motifs, which target the proteins to distinct subcellular compartments. OSBP homologues have been implicated in a wide range of intracellular processes, including vesicle trafficking, lipid metabolism and cell signaling, but little is known about the functional mechanisms of these proteins. The human family of OSBP homologues consists of twelve OSBP-related proteins (ORP). This thesis work is focused on one of the family members, ORP1, of which two variants were found to be expressed tissue-specifically in humans. The shorter variant, ORP1S contains an ORD only. The N-terminally extended variant, ORP1L, comprises a pleckstrin homology domain and three ankyrin repeats in addition to the ORD. The two ORP1 variants differ in intracellular localization. ORP1S is cytosolic, while the ankyrin repeat region of ORP1L targets the protein to late endosomes/lysosomes. This part of ORP1L also has profound effects on late endosomal morphology, inducing perinuclear clustering of late endosomes. A central aim of this study was to identify molecular interactions of ORP1L on late endosomes. The morphological changes of late endosomes induced by overexpressed ORP1L implies involvement of small Rab GTPases, regulators of organelle motility, tethering, docking and/or fusion, in generation of the phenotype. A direct interaction was demonstrated between ORP1L and active Rab7. ORP1L prolongs the active state of Rab7 by stabilizing its GTP-bound form. The clustering of late endosomes/lysosomes was also shown to be linked to the minus end-directed microtubule-based dynein-dynactin motor complex through the ankyrin repeat region of ORP1L. ORP1L, Rab7 and the Rab7-interacting lysosomal protein (RILP) were found to be part of the same effector complex recruiting the dynein-dynactin complex to late endosomes, thereby promoting minus end-directed movement. The proteins were found to be physically close to each other on late endosomes and RILP was found to stabilize the ORP1L-Rab7 interaction. It is possible that ORP1L and RILP bind to each other through their C-terminal and N-terminal regions, respectively, when they are bridged by Rab7. With the results of this study we have been able to place a member of the uncharacterized OSBP-family, ORP1L, in the endocytic pathway, where it regulates motility and possibly fusion of late endosomes through interaction with the small GTPase Rab7.