Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Tutkimus- ja kehitysyhteistyön motiivit

Pro gradu -tutkielman tavoitteena on operationalisoida T&K- yhteistyön prosessimaista luonnetta, eli tarkemmin sanottuna analysoida T&K-yhteistyösuhteidenmuodostumista ja motiiveja. Tutkielman hypoteesit muodostettiin analysoimalla yrityksen teknologiastrategiaan perustuvia uuden tiedon tuonnin ja olemassa olevan tiedon hyväksikäytön oppimistavoitteita. Motivaatio T&K- yhteistyölle syntyy mahdollisuudesta T&K- projektien riskien jakamiseen. T&K- yhteistyön motiiveja analysoitiin transaktio- ja byrokratiahyötyjen, jotka pohjautuvat mittakaava- ja synergiaeduille, lähteitä arvioiden. Hypoteeseja testattiin 276 suomalaisen teollisuusyrityksen otoksella. Otoksen yrityksillä oliollut T&K- toimintaa. Otos perustuu kyselyyn, joka toteutettiin Lappeenrannan teknillisen yliopiston kauppatieteiden osastolla vuonna 2004. Hypoteeseja testattiin tilastollisilla menetelmillä; lineaarisella regressioanalyysillä, parillisten ja riippumattomien otosten t-testeillä. Validiteetti- ja multikollineaarisuusongelman todennäköisyydet on huomioitu. Hypoteesit vahvistuivat osittain. Teknologisella epävarmuudella ja monimutkaisuudella ei ole suoraa vaikutusta T&K- yhteistyön intensiivisyyteen. Teknologisella epävarmuudella on osittainen vaikutus teknologiastrategian valintaan. Yrityksen transaktio- ja byrokratiahyödyt riippuvat teknologisista kyvykkyyksistä. Vain korkean teknologian alan yritykset saavuttavat hyötyjä myös intensiivisesti T&K- yhteistyösuhteita koordinoimalla. Teknologiaintensiivisyyteen perustuvien erot perustuvat teknologisen tiedon luonteeseen toimialalla. Transaktiokustannusteorian mukainenkustannusten minimointi ja kompetenssiperusteisten teorioiden mukainen strategisointi selittävät komplementaarisesti T&K-yhteistyösuhteiden muodostumista ja yrityksen rajojen määräytymistä.

Potentiometric titration as a method of determining the stoichiometric dissociation constants of weak acids from the thermodynamic dissociation constants of aqueous solutions at 298.15 K

The simple single-ion activity coefficient equation originating from the Debye-Hückel theory was used to determine the thermodynamic and stoichiometric dissociation constants of weak acids from data concerning galvanic cells. Electromotive force data from galvanic cells without liquid junctions, which was obtained from literature, was studied in conjuction with the potentiometric titration data relating to aqueous solutions at 298.15 K. The dissociation constants of weak acids could be determined by the presented techniques and almost all the experimental data studied could be interpreted within the range of experimental error. Potentiometric titration has been used here and the calculation methods were developed to obtain the thermodynamic and stoichiometric dissociation constants of some weak acids in aqueous solutions at 298.15 K. The ionic strength of titrated solutions were adjusted using an inert electrolyte, namely, sodium or potassium chloride. Salt content alonedetermines the ionic strength. The ionic strength of the solutions studied varied from 0.059 mol kg-1 to 0.37 mol kg-1, and in some cases up to 1.0 mol kg-1. The following substances were investigated using potentiometric titration: aceticacid, propionic acid, L-aspartic acid, L-glutamic acid and bis(2,2-dimethyl-3-oxopropanol) amine.