Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

Towards a predictive model of Ca²⁺ puffs

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca²⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca²⁺ concentrations eliminate Ca²⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca²⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca²⁺ puffs and hence the stochastic time scale of intracellular Ca²⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca²⁺ oscillations.

Why are some cyano-based ionic liquids better glucose solvents than water?

Among different classes of ionic liquids (ILs), those with cyano-based anions have been of special interest due to their low viscosity and enhanced solvation ability for a large variety of compounds. Experimental results from this work reveal that the solubility of glucose in some of these ionic liquids may be higher than in water – a well-known solvent with enhanced capacity to dissolve mono- and disaccharides. This raises questions on the ability of cyano groups to establish strong hydrogen bonds with carbohydrates and on the optimal number of cyano groups at the IL anion that maximizes the solubility of glucose. In addition to experimental solubility data, these questions are addressed in this study using a combination of density functional theory (DFT) and molecular dynamics (MD) simulations. Through the calculation of the number of hydrogen bonds, coordination numbers, energies of interaction and radial and spatial distribution functions, it was possible to explain the experimental results and to show that the ability to favorably interact with glucose is driven by the polarity of each IL anion, with the optimal anion being dicyanamide.

Probabilistic methods for seasonal forecasting in a changing climate: Cox-type regression models.

For climate risk management, cumulative distribution functions (CDFs) are an important source of information. They are ideally suited to compare probabilistic forecasts of primary (e.g. rainfall) or secondary data (e.g. crop yields). Summarised as CDFs, such forecasts allow an easy quantitative assessment of possible, alternative actions. Although the degree of uncertainty associated with CDF estimation could influence decisions, such information is rarely provided. Hence, we propose Cox-type regression models (CRMs) as a statistical framework for making inferences on CDFs in climate science. CRMs were designed for modelling probability distributions rather than just mean or median values. This makes the approach appealing for risk assessments where probabilities of extremes are often more informative than central tendency measures. CRMs are semi-parametric approaches originally designed for modelling risks arising from time-to-event data. Here we extend this original concept beyond time-dependent measures to other variables of interest. We also provide tools for estimating CDFs and surrounding uncertainty envelopes from empirical data. These statistical techniques intrinsically account for non-stationarities in time series that might be the result of climate change. This feature makes CRMs attractive candidates to investigate the feasibility of developing rigorous global circulation model (GCM)-CRM interfaces for provision of user-relevant forecasts. To demonstrate the applicability of CRMs, we present two examples for El Ni ? no/Southern Oscillation (ENSO)-based forecasts: the onset date of the wet season (Cairns, Australia) and total wet season rainfall (Quixeramobim, Brazil). This study emphasises the methodological aspects of CRMs rather than discussing merits or limitations of the ENSO-based predictors.

The Califa and Hipass circular velocity function for all morphological galaxy types

The velocity function (VF) is a fundamental observable statistic of the galaxy population that is similar to the luminosity function in importance, but much more difficult to measure. In this work we present the first directly measured circular VF that is representative between 60 < v_circ < 320 km s^-1 for galaxies of all morphological types at a given rotation velocity. For the low-mass galaxy population (60 < v_circ < 170 km s^-1), we use the HI Parkes All Sky Survey VF. For the massive galaxy population (170 < v_circ < 320 km s^-1), we use stellar circular velocities from the Calar Alto Legacy Integral Field Area Survey (CALIFA). In earlier work we obtained the measurements of circular velocity at the 80% light radius for 226 galaxies and demonstrated that the CALIFA sample can produce volume-corrected galaxy distribution functions. The CALIFA VF includes homogeneous velocity measurements of both late and early-type rotation-supported galaxies and has the crucial advantage of not missing gas-poor massive ellipticals that HI surveys are blind to. We show that both VFs can be combined in a seamless manner, as their ranges of validity overlap. The resulting observed VF is compared to VFs derived from cosmological simulations of the z = 0 galaxy population. We find that dark-matter-only simulations show a strong mismatch with the observed VF. Hydrodynamic simulations fare better, but still do not fully reproduce observations.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Analysis of electricity distribution network operation business models and capitalization of control room functions with DMS

Electricity distribution network operation (NO) models are challenged as they are expected to continue to undergo changes during the coming decades in the fairly developed and regulated Nordic electricity market. Network asset managers are to adapt to competitive technoeconomical business models regarding the operation of increasingly intelligent distribution networks. Factors driving the changes for new business models within network operation include: increased investments in distributed automation (DA), regulative frameworks for annual profit limits and quality through outage cost, increasing end-customer demands, climatic changes and increasing use of data system tools, such as Distribution Management System (DMS). The doctoral thesis addresses the questions a) whether there exist conditions and qualifications for competitive markets within electricity distribution network operation and b) if so, identification of limitations and required business mechanisms. This doctoral thesis aims to provide an analytical business framework, primarily for electric utilities, for evaluation and development purposes of dedicated network operation models to meet future market dynamics within network operation. In the thesis, the generic build-up of a business model has been addressed through the use of the strategicbusiness hierarchy levels of mission, vision and strategy for definition of the strategic direction of the business followed by the planning, management and process execution levels of enterprisestrategy execution. Research questions within electricity distribution network operation are addressed at the specified hierarchy levels. The results of the research represent interdisciplinary findings in the areas of electrical engineering and production economics. The main scientific contributions include further development of the extended transaction cost economics (TCE) for government decisions within electricity networks and validation of the usability of the methodology for the electricity distribution industry. Moreover, DMS benefit evaluations in the thesis based on the outage cost calculations propose theoretical maximum benefits of DMS applications equalling roughly 25% of the annual outage costs and 10% of the respective operative costs in the case electric utility. Hence, the annual measurable theoretical benefits from the use of DMS applications are considerable. The theoretical results in the thesis are generally validated by surveys and questionnaires.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Constraining the nuclear gluon distribution in eA processes at RHIC

A systematic determination of the gluon distribution is of fundamental interest in understanding the parton structure Of nuclei and the QCD dynamics. Currently, the behavior of this distribution at small x (high energy) is completely undefined. In this Letter we analyze the possibility of constraining the nuclear effects present in Xg(A) using the inclusive observables which would be measured in the future electron-nucleus collider at RHIC. We demonstrate that the Study of nuclear longitudinal and charm structure functions allows to estimate the magnitude of shadowing and antishadowing effects in the nuclear gluon distribution. (C) 2008 Elsevier B.V. All rights reserved.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Charm and longitudinal structure functions within the Kharzeev-Levin-Nardi model

We use the Kharzeev-Levin-Nardi (KLN) model of the low x gluon distributions to fit recent HERA data on F(L) and F(2)(c)(F(2)(b)). Having checked that this model gives a good description of the data, we use it to predict F(L) and F(2)(c) to be measured in a future electron-ion collider. The results are similar to those obtained with the de Florian-Sassot and Eskola-Paukkunen-Salgado nuclear gluon distributions. The conclusion of this exercise is that the KLN model, simple as it is, may still be used as an auxiliary tool to make estimates for both heavy-ion and electron-ion collisions.

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

A simple and effective inverse projection scheme for void distribution control in topology optimization

The ability to control both the minimum size of holes and the minimum size of structural members are essential requirements in the topology optimization design process for manufacturing. This paper addresses both requirements by means of a unified approach involving mesh-independent projection techniques. An inverse projection is developed to control the minimum hole size while a standard direct projection scheme is used to control the minimum length of structural members. In addition, a heuristic scheme combining both contrasting requirements simultaneously is discussed. Two topology optimization implementations are contributed: one in which the projection (either inverse or direct) is used at each iteration; and the other in which a two-phase scheme is explored. In the first phase, the compliance minimization is carried out without any projection until convergence. In the second phase, the chosen projection scheme is applied iteratively until a solution is obtained while satisfying either the minimum member size or minimum hole size. Examples demonstrate the various features of the projection-based techniques presented.