Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Real-time monitoring of the silicidation process of tungsten filaments at high temperature used as catalysers for silane decomposition

The scope of this work is the systematic study of the silicidation process affecting tungsten filaments at high temperature (1900ºC) used for silane decomposition in the hot-wire chemical vapour deposition technique (HWCVD). The correlation between the electrical resistance evolution of the filaments, Rfil(t), and the different stages of the their silicidation process is exposed. Said stages correspond to: the rapid formation of two WSi2 fronts at the cold ends of the filaments and their further propagation towards the middle of the filaments; and, regarding the hot central portion of the filaments: a initial stage of silicon dissolution into the tungsten bulk, with a random duration for as-manufactured filaments, followed by the inhomogeneous nucleation of W5Si3 (which is later replaced by WSi2) and its further growth towards the filaments core. An electrical model is used to obtain real-time information about the current status of the filaments silicidation process by simply monitoring their Rfil(t) evolution during the HWCVD process. It is shown that implementing an annealing pre-treatment to the filaments leads to a clearly repetitive trend in the monitored Rfil(t) signatures. The influence of hydrogen dilution of silane on the filaments silicidation process is also discussed.

Multidelayed random walks: Theory and application to the neolithic transition in Europe

We present a model in which particles (or individuals of a biological population) disperse with a rest time between consecutive motions (or migrations) which may take several possible values from a discrete set. Particles (or individuals) may also react (or reproduce). We derive a new equation for the effective rest time T˜ of the random walk. Application to the neolithic transition in Europe makes it possible to derive more realistic theoretical values for its wavefront speed than those following from the single-delayed framework presented previously [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)]. The new results are consistent with the archaeological observations of this important historical process

Optimization of KOH etching process to obtain textured substrates suitable for heterojunction solar cells fabricated by HWCVD

In this work, we have studied the texturization process of (100) c-Si wafers using a low concentration potassium hydroxide solution in order to obtain good quality textured wafers. The optimization of the etching conditions have led to random but uniform pyramidal structures with good optical properties. Then, symmetric heterojunctions were deposited by Hot-Wire CVD onto these substrates and the Quasi-Steady-State PhotoConductance technique was used to measure passivation quality. Little degradation in the effective lifetime and implicit open circuit voltage of these devices (< 20 mV) was observed in all cases. It is especially remarkable that for big uniform pyramids, the open-circuit voltage is comparable to the values obtained on flat substrates.

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Tool-supported invariant-based programming

The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.

Computational studies for the design of process equipment with complex geometries

This study combines several projects related to the flows in vessels with complex shapes representing different chemical apparata. Three major cases were studied. The first one is a two-phase plate reactor with a complex structure of intersecting micro channels engraved on one plate which is covered by another plain plate. The second case is a tubular microreactor, consisting of two subcases. The first subcase is a multi-channel two-component commercial micromixer (slit interdigital) used to mix two liquid reagents before they enter the reactor. The second subcase is a micro-tube, where the distribution of the heat generated by the reaction was studied. The third case is a conventionally packed column. However, flow, reactions or mass transfer were not modeled. Instead, the research focused on how to describe mathematically the realistic geometry of the column packing, which is rather random and can not be created using conventional computeraided design or engineering (CAD/CAE) methods. Several modeling approaches were used to describe the performance of the processes in the considered vessels. Computational fluid dynamics (CFD) was used to describe the details of the flow in the plate microreactor and micromixer. A space-averaged mass transfer model based on Fick’s law was used to describe the exchange of the species through the gas-liquid interface in the microreactor. This model utilized data, namely the values of the interfacial area, obtained by the corresponding CFD model. A common heat transfer model was used to find the heat distribution in the micro-tube. To generate the column packing, an additional multibody dynamic model was implemented. Auxiliary simulation was carried out to determine the position and orientation of every packing element in the column. This data was then exported into a CAD system to generate desirable geometry, which could further be used for CFD simulations. The results demonstrated that the CFD model of the microreactor could predict the flow pattern well enough and agreed with experiments. The mass transfer model allowed to estimate the mass transfer coefficient. Modeling for the second case showed that the flow in the micromixer and the heat transfer in the tube could be excluded from the larger model which describes the chemical kinetics in the reactor. Results of the third case demonstrated that the auxiliary simulation could successfully generate complex random packing not only for the column but also for other similar cases.

New stimuli-responsive block random copolymers and their aggregation

Les polymères sensibles à des stimuli ont été largement étudiés ces dernières années notamment en vue d’applications biomédicales. Ceux-ci ont la capacité de changer leurs propriétés de solubilité face à des variations de pH ou de température. Le but de cette thèse concerne la synthèse et l’étude de nouveaux diblocs composés de deux copolymères aléatoires. Les polymères ont été obtenus par polymérisation radicalaire contrôlée du type RAFT (reversible addition-fragmentation chain-transfer). Les polymères à bloc sont formés de monomères de méthacrylates et/ou d’acrylamides dont les polymères sont reconnus comme thermosensibles et sensible au pH. Premièrement, les copolymères à bloc aléatoires du type AnBm-b-ApBq ont été synthétisés à partir de N-n-propylacrylamide (nPA) et de N-ethylacrylamide (EA), respectivement A et B, par polymérisation RAFT. La cinétique de copolymérisation des poly(nPAx-co-EA1-x)-block-poly(nPAy-co-EA1-y) et leur composition ont été étudiées afin de caractériser et évaluer les propriétés physico-chimiques des copolymères à bloc aléatoires avec un faible indice de polydispersité . Leurs caractères thermosensibles ont été étudiés en solution aqueuse par spectroscopie UV-Vis, turbidimétrie et analyse de la diffusion dynamique de la lumière (DLS). Les points de trouble (CP) observés des blocs individuels et des copolymères formés démontrent des phases de transitions bien définies lors de la chauffe. Un grand nombre de macromolécules naturels démontrent des réponses aux stimuli externes tels que le pH et la température. Aussi, un troisième monomère, 2-diethylaminoethyl methacrylate (DEAEMA), a été ajouté à la synthèse pour former des copolymères à bloc , sous la forme AnBm-b-ApCq , et qui offre une double réponse (pH et température), modulable en solution. Ce type de polymère, aux multiples stimuli, de la forme poly(nPAx-co-DEAEMA1-x)-block-poly(nPAy-co-EA1-y), a lui aussi été synthétisé par polymérisation RAFT. Les résultats indiquent des copolymères à bloc aléatoires aux propriétés physico-chimiques différentes des premiers diblocs, notamment leur solubilité face aux variations de pH et de température. Enfin, le changement d’hydrophobie des copolymères a été étudié en faisant varier la longueur des séquences des blocs. Il est reconnu que la longueur relative des blocs affecte les mécanismes d’agrégation d’un copolymère amphiphile. Ainsi avec différents stimuli de pH et/ou de température, les expériences effectuées sur des copolymères à blocaléatoires de différentes longueurs montrent des comportements d’agrégation intéressants, évoluant sous différentes formes micellaires, d’agrégats et de vésicules.

The psychophysics of decision making in a two-direction random dot motion target selection task

La tâche de kinématogramme de points aléatoires est utilisée avec le paradigme de choix forcé entre deux alternatives pour étudier les prises de décisions perceptuelles. Les modèles décisionnels supposent que les indices de mouvement pour les deux alternatives sont encodés dans le cerveau. Ainsi, la différence entre ces deux signaux est accumulée jusqu’à un seuil décisionnel. Cependant, aucune étude à ce jour n’a testé cette hypothèse avec des stimuli contenant des mouvements opposés. Ce mémoire présente les résultats de deux expériences utilisant deux nouveaux stimuli avec des indices de mouvement concurrentiels. Parmi une variété de combinaisons d’indices concurrentiels, la performance des sujets dépend de la différence nette entre les deux signaux opposés. De plus, les sujets obtiennent une performance similaire avec les deux types de stimuli. Ces résultats supportent un modèle décisionnel basé sur l’accumulation des indices de mouvement net et suggèrent que le processus décisionnel peut intégrer les signaux de mouvement à partir d’une grande gamme de directions pour obtenir un percept global de mouvement.

Novel Melt Transurethane Process for Cycloaliphatic Polyurethanes and Their Self-Organization for Nano-Materials

In this introduction part, importance has been given to the elastomeric properties of polyurethanes. Emphasis has been laid to this property based on microphase separation and how this could be modified by modifying the segment lengths, as well as the structure of the segments. Implication was also made on the mechanical and thermal properties of these copolymers based on various analytical methods usually used for characterization of polymers. A brief overview of the challenges faced by the polyurethane chemistry was also done, pointing to the fact that though polyurethane industry is more than 75 years old, still a lot of questions remain unanswered, that too mostly in the synthesis of polyurethanes. A major challenge in this industry is the utilization of more environmental friendly “Green Chemistry Routes” for the synthesis of polyurethanes which are devoid of any isocyanates or harsh solvents.The research work in this thesis was focused to develop non-isocyanate green chemical process for polyurethanes and also self-organize the resultant novel polymers into nano-materials. The thesis was focused on the following three major aspects:(i) Design and development of novel melt transurethane process for polyurethanes under non-isocyanate and solvent free melt condition. (ii) Solvent induced self-organization of the novel cycloaliphatic polyurethanes prepared by the melt transurethane process into microporous templates and nano-sized polymeric hexagons and spheres. (iii) Novel polyurethane-oligophenylenevinylene random block copolymer nano-materials and their photoluminescence properties. The second chapter of the thesis gives an elaborate discussion on the “Novel Melt Transurethane Process ” for the synthesis of polyurethanes under non-isocyanate and solvent free melt condition. The polycondensation reaction was carried out between equimolar amounts of a di-urethane monomer and a diol in the presence of a catalyst under melt condition to produce polyurethanes followed by the removal of low boiling alcohol from equilibrium. The polymers synthesized through this green chemical route were found to be soluble (devoid of any cross links), thermally stable and free from any isocyanate entities. The polymerization reaction was confirmed by various analytical techniques with specific references to the extent of reaction which is the main watchful point for any successful polymerization reaction. The mechanistic aspects of the reaction were another point of consideration for the novel polymerization route which was successfully dealt with by performing various model reactions. Since this route was successful enough in synthesizing polyurethanes with novel structures, they were employed for the solvent induced self-organization which is an important area of research in the polymer world in the present scenario. Chapter three mesmerizes the reader with multitudes of morphologies depending upon the chemical backbone structure of the polyurethane as well as on the nature and amount of various solvents employed for the self-organization tactics. The rationale towards these morphologies-“Hydrogen Bonding ” have been systematically probed by various techniques. These polyurethanes were then tagged with luminescent 0ligo(phenylene vinylene) units and the effects of these OPV blocks on the morphology of the polyurethanes were analyzed in chapter four. These blocks have resulted in the formation of novel “Blue Luminescent Balls” which could find various applications in optoelectronic devices as well as delivery vehicles.

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space