On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Adaptive coatings based on polyaniline for direct 2D observation of diffusion processes in microfluidic systems

[EN] Therefore the understanding and proper evaluation of the flow and mixing behaviour at microscale becomes a very important issue. In this study, the diffusion behaviour of two reacting solutions of HCI and NaOH were directly observed in a glass/polydimethylsiloxane microfluidic device using adaptive coatings based on the conductive polymer polyaniline that are covalently attached to the microchannel walls. The two liquid streams were combined at the junction of a Y-shaped microchannel, and allowed to diffuse into each other and react. The results showed excellent correlation between optical observation of the diffusion process and the numerical results. A numerical model which is based on finite volume method (FVM) discretisation of steady Navier-Stokes (fluid flow) equations and mass transport equations without reactions was used to calculate the flow variables at discrete points in the finite volume mesh element. The high correlation between theory and practical data indicates the potential of such coatings to monitor diffusion processes and mixing behaviour inside microfluidic channels in a dye free environment.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Derivations of variational gaussian process approximation framework

Recently, within the VISDEM project (EPSRC funded EP/C005848/1), a novel variational approximation framework has been developed for inference in partially observed, continuous space-time, diffusion processes. In this technical report all the derivations of the variational framework, from the initial work, are provided in detail to help the reader better understand the framework and its assumptions.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Diffusion dynamics on multiplex networks

We study the time scales associated with diffusion processes that take place on multiplex networks, i.e., on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which consists of a dimensional lifting of the Laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-Laplacian allows us to understand the physics of diffusionlike processes on top of multiplex networks.

Mobile Communications within the European Union: The Role of Location in the Evolution and Forecasting of the Diffusion Process

In the European Union, the importance of mobile communications was realized early on. The process of mobile communications becoming ubiquitous has taken time, as the innovation of mobile communications diffused into the society. The aim of this study is to find out how the evolution and spatial patterns of the diffusion of mobile communications within the European Union could be taken into account in forecasting the diffusion process. There is relatively lot of research of innovation diffusion on the individual (micro) andthe country (macro) level, if compared to the territorial level. Territorial orspatial diffusion refers either to the intra-country or inter-country diffusionof an innovation. In both settings, the dif- fusion of a technological innovation has gained scarce attention. This study adds knowledge of the diffusion between countries, focusing especially on the role of location in this process. The main findings of the study are the following: The penetration rates of the European Union member countries have become more even in the period of observation, from the year 1981 to 2000. The common digital GSM system seems to have hastened this process. As to the role of location in the diffusion process, neighboring countries have had similar diffusion processes. They can be grouped into three, the Nordic countries, the central and southern European countries, and the remote southern European countries. The neighborhood effect is also domi- nating in thegravity model which is used for modeling the adoption timing of the countries. The subsequent diffusion within a country, measured by the logistic model in Finland, is af- fected positively by its economic situation, and it seems to level off at some 92 %. Considering the launch of future mobile communications systemsusing a common standard should implicate an equal development between the countries. The launching time should be carefully selected as the diffusion is probably delayed in economic downturns. The location of a country, measured by distance, can be used in forecasting the adoption and diffusion. Fi- nally, the result of penetration rates becoming more even implies that in a relatively homoge- nous set of countries, such as the European Union member countries, the estimated final pene- tration of a single country can be used for approximating the penetration of the others. The estimated eventual penetration of Finland, some 92 %, should thus also be the eventual level for all the European Union countries and for the European Union as a whole.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.

Speziation von Plutonium bei der Sorption und Diffusion in Opalinuston

Die vorliegende Arbeit wurde im Rahmen des BMWi-Verbundprojektes Wechselwirkung und Transport von Aktiniden im natürlichen Tongestein unter Berücksichtigung von Huminstoffen und Tonorganika – Wechselwirkung von Neptunium und Plutonium mit natürlichem Tongestein“ durchgeführt. Um die langfristige Sicherheit der nuklearen Endlager beurteilen zu können, muss eine mögliche Migration der radiotoxischen Abfälle in die Umwelt betrachtet werden. Wegen seiner langen Halbwertszeit (24000 a) leistet Pu-239 einen wesentlichen Beitrag zur Radiotoxizität abgebrannter Kernbrennstoffe in einem Endlager. Das redox-sensitive Pu tritt in Lösung unter umweltrelevanten Bedingungen in den Oxidationsstufen +III bis +VI auf und kann nebeneinander in bis zu vier Oxidationsstufen vorliegen. Tonsteinformationen werden als mögliches Wirtsgestein für Endlager hoch-radioaktiver Abfälle betrachtet. Deshalb sind ausführliche Informationen zur Mobilisierung und Immobilisierung des Pu durch/in das Grundwasser aus einem Endlager von besonderer Bedeutung. In dieser Arbeit wurden neue Erkenntnisse über die Wechselwirkung zwischen Pu und dem natürlichen Tongestein Opalinuston (OPA, Mont Terri, Schweiz) mit Hinblick auf die Endlagerung wärmeentwickelnder radioaktiver Abfälle in einem geologischen Tiefenlager gewonnen.rnDer Fokus der Arbeit lag dabei auf der Bestimmung der Speziation von Pu an der Mineraloberfläche nach Sorptions- und Diffusionsprozessen mittels verschiedener synchrotronbasierter Methoden (µ-XRF, µ-XANES/EXAFS, µ-XRD, XANES/EXAFS). rnDie Wechselwirkung zwischen Pu und OPA wurde zunächst in Batch- und Diffusionsexperimenten in Abhängigkeit verschiedener experimenteller Parameter (u.a. pH, Pu-Oxidationsstufe) untersucht. In Sorptionsexperimenten konnte gezeigt werden, dass einige Parameter (z.B. Temperatur, Huminsäure) einen deutlichen Einfluss auf die Sorption von Pu haben.rnDie Speziationsuntersuchungen wurden zum einen an Pulverproben aus Batchexperimenten und zum anderen an OPA-Dünnschliffen bzw. Diffusionsproben in Abhängigkeit verschiedener experimenteller Parameter durchgeführt. Die EXAFS-Messungen an der Pu LIII-Kante der Pulverproben ergaben, dass eine innersphäriche Sorption von Pu(IV) an Tongestein unabhängig von dem Ausgangsoxidationszustand des Plutoniums in Lösung stattgefunden hat. Durch die Kombination der ortsaufgelösten Methoden wurde erstmalig mittels μ-XRF die Verteilung von Pu und anderen in OPA enthaltenen Elementen bestimmt. µ-XANES-Spektren an Pu-Anreicherungen auf OPA-Dünnschliffen und in Diffusionsproben bestätigen, dass das weniger mobile Pu(IV) die dominierende Spezies nach den Sorptions- und Diffusionsprozessen ist. Darüber hinaus wurde zum ersten Mal ein Diffusionsprofil von Pu in OPA mittels µ-XRF gemessen. Die Speziationsuntersuchungen mittels μ-XANES zeigten, dass das eingesetzte Pu(V) entlang seines Diffusionspfades zunehmend zu Pu(IV) reduziert wird. Mit µ-XRD wurde Illit als dominierende Umgebung, in der Pu angereichert wurde, identifiziert und Siderit als eine redoxaktive Phase auftreten kann. Die Ergebnisse dieser Arbeit zeigen, dass die Sicherheit von OPA als Wirtsgestein eines Endlagers hoch-radioaktiver Abfälle positiv zu bewerten ist. rn

Diffusion transport of water in basalts

Studying diffusive transport in porous rocks is of fundamental importance in understanding a variety of geochemical processes including: element transfer, primary mineral dissolution kinetics and precipitation of secondary phases. Here we report new findings on the relationship between diffusive transport and textural characteristics of the pore systems on the example of mid-oceanic ridge basalts having different degree of alteration but very similar bulk pore volume. Diffusion processes in porous basalts were studied in situ using H2O -> D2O exchange experiments. The effective diffusion coefficients of water molecules increase systematically from 5.05*10**-11 to 1.19*10**-10 m**2/s for fresh and moderately altered basalts and from 2.40*10**-11 to 6.72*10**-11 m**2/s for completely altered basalt as temperature increases from 5 to 50 °C. The activation energy of the diffusion process increases from 12.29 ± 0.71 kJ/mol for fresh and moderately altered basalts to 14.3 ± 1.33 kJ/mol for completely altered basalt. The results indicate that neither the bulk porosity nor the degree of alteration can be used as proxies for the efficiency of element transport during MORB-water interaction. The formation of secondary phases that replace primary minerals and fill the pore space in the rock leads to the formation of tiny pores and phases with large specific surface area. These factors might have a dominant control on the transport properties of altered basaltic rocks.

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25