Discrete Models of Time-Fractional Diffusion in a Potential Well

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

Microscopic generalization of the standard interacting boson model Hamiltonian in the restricted dynamics approach

The evaluation of the microscopic generalized interacting boson model (GIBM) Hamiltonian, deduced from the general microscopic nuclear Hamiltonian via the collective O-A-1 invariant microscopic Hamiltonian of the general restricted dynamics model (RDM) in the case of central multipole and multipole-Gauss type effective NN-potential is briefly discussed. The GIBM version, which includes all sixth-order terms in the expansion of the collective part of the NN-potential, has been obtained. This GIBM Hamiltonian contains additional terms compared with the standard (sd-boson) interacting boson model (IBM). The microscopic expressions for the standard IBM Hamiltonian parameters in terms of the employed effective NN-potential parameters have also been obtained.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by epsilon(AA) and by epsilon(AB) = r epsilon(AA), respectively. The angle theta between the 2 A-patches on each particle is fixed at 601, 90 degrees or 120 degrees. For values of r below 1/2 and above a threshold r(th)(theta) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when theta decreases. We show that the mechanism that prevents phase separation for models with decreasing values of theta is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings ( loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of theta, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Lean construction in rehabilitation works – suitability analysis and contribution for the definition of an implementation model

Proceedings IGLC-19, July 2011, Lima, Perú

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Rapid cohort generation and analysis of disease spectrum of large animal model of cone dystrophy.

Large animal models are an important resource for the understanding of human disease and for evaluating the applicability of new therapies to human patients. For many diseases, such as cone dystrophy, research effort is hampered by the lack of such models. Lentiviral transgenesis is a methodology broadly applicable to animals from many different species. When conjugated to the expression of a dominant mutant protein, this technology offers an attractive approach to generate new large animal models in a heterogeneous background. We adopted this strategy to mimic the phenotype diversity encounter in humans and generate a cohort of pigs for cone dystrophy by expressing a dominant mutant allele of the guanylate cyclase 2D (GUCY2D) gene. Sixty percent of the piglets were transgenic, with mutant GUCY2D mRNA detected in the retina of all animals tested. Functional impairment of vision was observed among the transgenic pigs at 3 months of age, with a follow-up at 1 year indicating a subsequent slower progression of phenotype. Abnormal retina morphology, notably among the cone photoreceptor cell population, was observed exclusively amongst the transgenic animals. Of particular note, these transgenic animals were characterized by a range in the severity of the phenotype, reflecting the human clinical situation. We demonstrate that a transgenic approach using lentiviral vectors offers a powerful tool for large animal model development. Not only is the efficiency of transgenesis higher than conventional transgenic methodology but this technique also produces a heterogeneous cohort of transgenic animals that mimics the genetic variation encountered in human patients.

Derivation of an observer model adapted to irregular signals based on convolution channels.

Anthropomorphic model observers are mathe- matical algorithms which are applied to images with the ultimate goal of predicting human signal detection and classification accuracy across varieties of backgrounds, image acquisitions and display conditions. A limitation of current channelized model observers is their inability to handle irregularly-shaped signals, which are common in clinical images, without a high number of directional channels. Here, we derive a new linear model observer based on convolution channels which we refer to as the "Filtered Channel observer" (FCO), as an extension of the channelized Hotelling observer (CHO) and the nonprewhitening with an eye filter (NPWE) observer. In analogy to the CHO, this linear model observer can take the form of a single template with an external noise term. To compare with human observers, we tested signals with irregular and asymmetrical shapes spanning the size of lesions down to those of microcalfications in 4-AFC breast tomosynthesis detection tasks, with three different contrasts for each case. Whereas humans uniformly outperformed conventional CHOs, the FCO observer outperformed humans for every signal with only one exception. Additive internal noise in the models allowed us to degrade model performance and match human performance. We could not match all the human performances with a model with a single internal noise component for all signal shape, size and contrast conditions. This suggests that either the internal noise might vary across signals or that the model cannot entirely capture the human detection strategy. However, the FCO model offers an efficient way to apprehend human observer performance for a non-symmetric signal.

Validation of plant dynamic model by online and laboratory measurements – a tool to predict online COD loads out of production of mechanical printing papers

COD discharges out of processes have increased in line with elevating brightness demands for mechanical pulp and papers. The share of lignin-like substances in COD discharges is on average 75%. In this thesis, a plant dynamic model was created and validated as a means to predict COD loading and discharges out of a mill. The assays were carried out in one paper mill integrate producing mechanical printing papers. The objective in the modeling of plant dynamics was to predict day averages of COD load and discharges out of mills. This means that online data, like 1) the level of large storage towers of pulp and white water 2) pulp dosages, 3) production rates and 4) internal white water flows and discharges were used to create transients into the balances of solids and white water, referred to as “plant dynamics”. A conversion coefficient was verified between TOC and COD. The conversion coefficient was used for predicting the flows from TOC to COD to the waste water treatment plant. The COD load was modeled with similar uncertainty as in reference TOC sampling. The water balance of waste water treatment was validated by the reference concentration of COD. The difference of COD predictions against references was within the same deviation of TOC-predictions. The modeled yield losses and retention values of TOC in pulping and bleaching processes and the modeled fixing of colloidal TOC to solids between the pulping plant and the aeration basin in the waste water treatment plant were similar to references presented in literature. The valid water balances of the waste water treatment plant and the reduction model of lignin-like substances produced a valid prediction of COD discharges out of the mill. A 30% increase in the release of lignin-like substances in the form of production problems was observed in pulping and bleaching processes. The same increase was observed in COD discharges out of waste water treatment. In the prediction of annual COD discharge, it was noticed that the reduction of lignin has a wide deviation from year to year and from one mill to another. This made it difficult to compare the parameters of COD discharges validated in plant dynamic simulation with another mill producing mechanical printing papers. However, a trend of moving from unbleached towards high-brightness TMP in COD discharges was valid.

Quantum dynamics of the parabolic model

Kvanttimekaniikan teoriassa suljettuja, ympäristöstään eristettyjä systeemejä koskevat tulokset ovat hyvin tunnettuja. Eräs tärkeä erityispiirre tällaisille systeemeille on, että niiden aikakehitys on unitaarista. Oletus siitä, että systeemi on suljettu, on osaltaan tietysti vain yksinkertaistus. Käytännössä kaikki kvanttimekaaniset systeemit vuorovaikuttavat ympäristönsä kanssa ja tästä johtuen niiden dynamiikka monimutkaistuu oleellisesti. Kuitenkin tietyissä tapauksissa systeemin aikakehitys voidaan ratkaista, ainakin approksimatiivisesti. Tärkeimpinä esimerkkeinä on ympäristön joko nopea tai erittäin hidas muutos kvanttisysteemin ominaiseen aikaskaalaan verrattuna. Näistä erityisesti jälkimmäinen on käyttökelpoinen oletus monissa fysikaalisissa tilanteissa. Tällöin voidaan suorittaa niin sanottu adiabaattinen approksimaatio. Sen mukaan systeemi, joka on aikakehityksen generoivan Hamiltonin operaattorin ominaistilassa, pysyy vastaavassa ominaistilassa ympäristön muuttuessa äärettömän hitaasti, mikäli systeemin eri energiatasot eivät leikkaa toisiaan. Todellisissa tilanteissa muutos ei tietenkään voi olla äärettömän hidasta ja myös energiatasojen leikkaukset ovat mahdollisia, jolloin tapahtuu transitio eri ominaistilojen välillä. Energiatasojen leikkauksilla on oleellisia vaikutuksia erittäin monissa fysikaalisissa prosesseissa ja niitä kuvaamaan on luotu monia malleja kvanttimekaniikan alkuajoista lähtien aina tähän päivään saakka. Nykyinen teknologinen kehitys on avannut uudenlaisen mahdollisuuden ilmiön kokeelliseen varmentamiseen ja hyödyntämiseen. Tämän vuoksi kyseisten mallien dynamiikan ja erityisesti energiatasojen useiden peräkkäisten leikkausten aiheuttamien koherenssi-ilmiöiden selvittäminen on tärkeää. Tässä työssä käsitellään kvanttimekaanisia kaksitasosysteemejä, joissa esiintyy energiatasojen leikkauksia sekä niiden pitkän aikavälin dynamiikkaa. Tutkielmassa perehdytään tarkemmin kahteen tiettyyn malliin. Näistä ensimmäinen, Landau-Zener -malli, on tunnetuin ja sovelluksissa käytetyin malli. Kuitenkin erityisen mielenkiinnon kohteena on niin kutsuttu parabolinen malli, jolle johdetaan eri approksimaatioita käyttäen asymptoottiset transitiotodennäköisyydet eri tilojen välille. Näitä verrataan numeerisiin tuloksiin.

Development of Generic Simulation Model for Mobile Working Machines

This master’s thesis has been done for Drive! –project in which a new electric motor solution for mobile working machines is developed. Generic simulation model will be used as marketing and development tool. It can be used to model a wide variety of different vehicles with and without electric motor and to show customer the difference between traditionally build vehicles and those with new electric motor solution. Customers can also use simulation model to research different solutions for their own vehicles. At the start of the project it was decided that MeVEA software would be used as main simulation program and Simulink will only be used to simulate the operation of electrical components. Development of the generic model started with the research of these two software applications, simulation models which are made with them and how these simulation models can be build faster. Best results were used for building of generic simulation model. Finished generic model can be used to produce new tractor models for real-time simulations in short notice. All information about model is collected to one datasheet which can be easily filled by the user. After datasheet is filled a script will automatically build new simulation model in seconds. At the moment generic model is capable of building simulation models for wide variety of different tractors but it can be easily altered for other vehicle types too which would also benefit greatly from electric drive solution. Those could be for example wheel loaders and harvesters.