Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Analyzing hydraulic head of fluid flow in underground porous medium

Hydraulic head is distributed through a medium with porous aspect. The analysis of hydraulic head from one point to another is used by the Richard's equation. This equation is equivalent to the groundwater ow equation that predicts the volumetric water contents. COMSOL 3.5 is used for computation applying Richard's equation. A rectangle of 100 meters of length and 10 meters of large (depth) with 0,1 m/s fl ux of inlet as source of our fl uid is simulated. The domain have Richards' equation model in two dimension (2D). Hydraulic head increases proportional with moisture content.

Best Practices of International Double Master's Degree Programmes: Comparative Study on Finnish and Russian Universities

The purpose of this report is to disseminate the best practices of double degree programmes’ organization, implementation and development between Russian and European universities. The findings reveal good developments in the field of double degree cooperation between Russian and European universities and a high motivation from both parties. The report depicts different models of building a joint curriculum and organizing academic mobility. Foreign language skills improvement for students and university staff, involvement of international companies, and joint strategy and actions in marketing and quality assurance are some redevelopments points recommended in the report.

Modulaarisen rakentamisen vaikutus liiketoimintaprosessiin - case kohdeorganisaatio

Backround of this master thesis is previously recognized possibility to build housing units by a new modular building method. This master thesis aims to examine how modular building method influences to business process in the case organization: how will the process change and to whom will the change influence. To examine this, there is a need to declare as-is and to-be processes and find out the changes of the process. Modular building method is a radical change when comparing it to existing. The findings are that modular building method will produce utility by repeating. It needs time and repeating to achieve the utilities. Ability to repeat demands working with more several phases than currently. Modular building method influences also to customer and his/her choices and because of that, it has influences to financial equation.

Modelling of hydrogen stratification and gas mixing in containment using the APROS code

Hydrogen stratification and atmosphere mixing is a very important phenomenon in nuclear reactor containments when severe accidents are studied and simulated. Hydrogen generation, distribution and accumulation in certain parts of containment may pose a great risk to pressure increase induced by hydrogen combustion, and thus, challenge the integrity of NPP containment. The accurate prediction of hydrogen distribution is important with respect to the safety design of a NPP. Modelling methods typically used for containment analyses include both lumped parameter and field codes. The lumped parameter method is universally used in the containment codes, because its versatility, flexibility and simplicity. The lumped parameter method allows fast, full-scale simulations, where different containment geometries with relevant engineering safety features can be modelled. Lumped parameter gas stratification and mixing modelling methods are presented and discussed in this master’s thesis. Experimental research is widely used in containment analyses. The HM-2 experiment related to hydrogen stratification and mixing conducted at the THAI facility in Germany is calculated with the APROS lump parameter containment package and the APROS 6-equation thermal hydraulic model. The main purpose was to study, whether the convection term included in the momentum conservation equation of the 6-equation modelling gives some remarkable advantages compared to the simplified lumped parameter approach. Finally, a simple containment test case (high steam release to a narrow steam generator room inside a large dry containment) was calculated with both APROS models. In this case, the aim was to determine the extreme containment conditions, where the effect of convection term was supposed to be possibly high. Calculation results showed that both the APROS containment and the 6-equation model could model the hydrogen stratification in the THAI test well, if the vertical nodalisation was dense enough. However, in more complicated cases, the numerical diffusion may distort the results. Calculation of light gas stratification could be probably improved by applying the second order discretisation scheme for the modelling of gas flows. If the gas flows are relatively high, the convection term of the momentum equation is necessary to model the pressure differences between the adjacent nodes reasonably.

Adaptive control of Hydraulic Drive

Adaptive control systems are one of the most significant research directions of modern control theory. It is well known that every mechanical appliance’s behavior noticeably depends on environmental changes, functioning-mode parameter changes and changes in technical characteristics of internal functional devices. An adaptive controller involved in control process allows reducing an influence of such changes. In spite of this such type of control methods is applied seldom due to specifics of a controller designing. The work presented in this paper shows the design process of the adaptive controller built by Lyapunov’s function method for the Hydraulic Drive. The calculation needed and the modeling were conducting with MATLAB® software including Simulink® and Symbolic Math Toolbox™ etc. In the work there was applied the Jacobi matrix linearization of the object’s mathematical model and derivation of the suitable reference models based on Newton’s characteristic polynomial. The intelligent adaptive to nonlinearities algorithm for solving Lyapunov’s equation was developed. Developed algorithm works properly but considered plant is not met requirement of functioning with. The results showed confirmation that adaptive systems application significantly increases possibilities in use devices and might be used for correction a system’s behavior dynamics.

Modelling of ultrasound assisted mixing in Newtonian and non-Newtonian liquids

The purpose of this work is to obtain a better understanding of behaviour of possible ultrasound appliance on fluid media mixing. The research is done in the regard to Newtonian and non-Newtonian fluids. The process of ultrasound appliance on liquids is modelled in COMSOL Multiphysics software. The influence of ultrasound using is introduced as waveform equation. Turbulence modelling is fulfilled by the k-ε model in Newtonian fluid. The modeling of ultrasound assisted mixing in non-Newtonian fluids is based on the power law. To verify modelling results two practical methods are used: Particle Image Velocimetry and measurements of mixing time. Particle Image Velocimetry allows capturing of velocity flow field continuously and presents detailed depiction of liquid dynamics. The second way of verification is the comparison of mixing time of homogeneity. Experimentally achievement of mixing time is done by conductivity measurements. In modelling part mixing time is achieved by special module of COMSOL Multiphysics – the transport of diluted species. Both practical and modelling parts show similar radial mechanism of fluid flow under ultrasound appliance – from the horn tip fluid moves to the bottom and along the walls goes back. Velocity profiles are similar in modelling and experimental part in the case of Newtonian fluid. In the case of non-Newtonian fluid velocity profiles do not agree. The development track of ultrasound-assisted mixing modelling is presented in the thesis.

Glucocorticoids, master modulators of the thymic catecholaminergic system?

There is evidence that the major mediators of stress, i.e., catecholamines and glucocorticoids, play an important role in modulating thymopoiesis and consequently immune responses. Furthermore, there are data suggesting that glucocorticoids influence catecholamine action. Therefore, to assess the putative relevance of glucocorticoid-catecholamine interplay in the modulation of thymopoiesis we analyzed thymocyte differentiation/maturation in non-adrenalectomized and andrenalectomized rats subjected to treatment with propranolol (0.4 mg·100 g body weight-1·day-1) for 4 days. The effects of β-adrenoceptor blockade on thymopoiesis in non-adrenalectomized rats differed not only quantitatively but also qualitatively from those in adrenalectomized rats. In adrenalectomized rats, besides a more efficient thymopoiesis [judged by a more pronounced increase in the relative proportion of the most mature single-positive TCRαβhigh thymocytes as revealed by two-way ANOVA; for CD4+CD8- F (1,20) = 10.92, P < 0.01; for CD4-CD8+ F (1,20) = 7.47, P < 0.05], a skewed thymocyte maturation towards the CD4-CD8+ phenotype, and consequently a diminished CD4+CD8-/CD4-CD8+ mature TCRαβhigh thymocyte ratio (3.41 ± 0.21 in non-adrenalectomized rats vs 2.90 ± 0.31 in adrenalectomized rats, P < 0.05) were found. Therefore, we assumed that catecholaminergic modulation of thymopoiesis exhibits a substantial degree of glucocorticoid-dependent plasticity. Given that glucocorticoids, apart from catecholamine synthesis, influence adrenoceptor expression, we also hypothesized that the lack of adrenal glucocorticoids affected not only β-adrenoceptor- but also α-adrenoceptor-mediated modulation of thymopoiesis.

Use of the Wasserman equation in optimization of the duration of the power ramp in a cardiopulmonary exercise test: a study of Brazilian men

This study aimed to analyze the agreement between measurements of unloaded oxygen uptake and peak oxygen uptake based on equations proposed by Wasserman and on real measurements directly obtained with the ergospirometry system. We performed an incremental cardiopulmonary exercise test (CPET), which was applied to two groups of sedentary male subjects: one apparently healthy group (HG, n=12) and the other had stable coronary artery disease (n=16). The mean age in the HG was 47±4 years and that in the coronary artery disease group (CG) was 57±8 years. Both groups performed CPET on a cycle ergometer with a ramp-type protocol at an intensity that was calculated according to the Wasserman equation. In the HG, there was no significant difference between measurements predicted by the formula and real measurements obtained in CPET in the unloaded condition. However, at peak effort, a significant difference was observed between oxygen uptake (V˙O2)peak(predicted)and V˙O2peak(real)(nonparametric Wilcoxon test). In the CG, there was a significant difference of 116.26 mL/min between the predicted values by the formula and the real values obtained in the unloaded condition. A significant difference in peak effort was found, where V˙O2peak(real)was 40% lower than V˙O2peak(predicted)(nonparametric Wilcoxon test). There was no agreement between the real and predicted measurements as analyzed by Lin’s coefficient or the Bland and Altman model. The Wasserman formula does not appear to be appropriate for prediction of functional capacity of volunteers. Therefore, this formula cannot precisely predict the increase in power in incremental CPET on a cycle ergometer.

Voimalaitoksen energiaraportoinnin kehittäminen

Diplomityössä tarkasteltiin Metsä Board Simpeleen voimalaitoksen energiaraportointi kokonaisuutta. Tarkastelun kohteena olivat lämpö-, sähkö- ja polttoaine-energiat. Tarkastelun pääpaino oli energian määritykseen tarvittavissa mittapisteissä sekä niistä muodostuvissa raporteissa. Työn tavoitteena oli saada luotettavat energiaraportit, jotka ovat jaoteltu selkeästi ja johdonmukaisesti. Tavoitteena oli myös vähentää kuukausiraportoinnin muodostamiseen tarvittavaa henkilötyöaikaa. Teoriaosuudessa käsitellään yleisesti voimalaitosprosessin toimintaa sekä siinä käytettäviä polttoaineita. Energiataseen muodostamisen perusteita tarkasteltiin voimalaitosprosessin kannalta. Energian määrityksiin käytettävät prosessimittaukset käytiin läpi. Raportointivelvollisuudet selvitettiin, niin tilastokeskuksien, kuin viranomaistenkin suuntaan. Työosuudessa perehdyttiin käytössä oleviin raportointikäytäntöihin sekä raporttipohjiin. Energialaskentayhtälöt ja parametrit tarkastettiin tarvittavilta osin. Työnaikana havaittiin nopeasti, että raportointi muodostetaan pitkälti Microsoft Excel-taulukkolaskentaohjelmiston avulla. Olemassa olevia automatisoituja raportteja ei hyödynnetty ollenkaan, koska niitä pidettiin epäluotettavina. Työn tuloksena automatisoidut kuukausiraportit tarkastettiin, virheet korjattiin ja ne otettiin käyttöön. Automaattisiin raportteihin tehtiin päivitysehdotukset uusista raporttipohjista. Viralliseen kuukausiraportointiin rakennettiin myös kokonaan uudet raportointipohjat, jotka hyödyntävät automaattisesti muodostuvia raportteja. Uudet raporttipohjat nopeuttivat raportointityötä merkittävästi. Polttoaine-energian hallintajärjestelmä todettiin vanhanaikaiseksi ja sen uusimista suositellaan. Uusinnalla raportointityö helpottuisi ja sen avulla siitä saataisiin kattavampi.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

A Critical Analysis of the Philosophical-Political Element of the Master-Slave Dialectic

ABSTRACT:The section “Lordship and Bondage” in Hegel’s Phenomenology of Spirit offers us, through the criticism of slavery, some indications regarding Hegel’s conception of human nature. In this paper some consequences of this conception for Hegel’s political philosophy are identified and presented. The analysis shows problems may emerge when we analyze some fundamental Hegelian concepts – “recognition” and shows that some “men” – if we take into consideration the way these concepts were defined in the master-slave dialectic. In light of these problems it is pointed out that Hegel’s political philosophy, and also his position regarding slavery, become less cogent and more susceptible to criticism. The last part of the text analyzes some consequences of problems related to the possibility of defining the concepts “recognition” and “men” in terms of Hegel’s model of state.

Modelling the exothermic heat and the demand of cooling in paper and pulp industry biological wastewater treatment

This master thesis presents a study on the requisite cooling of an activated sludge process in paper and pulp industry. The energy consumption of paper and pulp industry and it’s wastewater treatment plant in particular is relatively high. It is therefore useful to understand the wastewater treatment process of such industries. The activated sludge process is a biological mechanism which degrades carbonaceous compounds that are present in waste. The modified activated sludge model constructed here aims to imitate the bio-kinetics of an activated sludge process. However, due to the complicated non-linear behavior of the biological process, modelling this system is laborious and intriguing. We attempt to find a system solution first using steady-state modelling of Activated Sludge Model number 1 (ASM1), approached by Euler’s method and an ordinary differential equation solver. Furthermore, an enthalpy study of paper and pulp industry’s vital pollutants was carried out and applied to revise the temperature shift over a period of time to formulate the operation of cooling water. This finding will lead to a forecast of the plant process execution in a cost-effective manner and management of effluent efficiency. The final stage of the thesis was achieved by optimizing the steady state of ASM1.