A method of fundamental solutions for the one-dimensional inverse Stefan problem

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Advanced oxidation of arsenic species in aqueous solutions

Ingestion of arsenic from contaminated water is a serious problem and affects the health of more than 100 million people worldwide. Traditional water purification technologies are generally not effective or cost prohibitive for the removal of arsenic to acceptable levels (≤10 ppb). Current multi-step arsenic removal processes involve oxidation, precipitation and/or adsorption. Advanced Oxidation Technologies (AOTs) may be attractive alternatives to existing treatments. The reactions of inorganic and organic arsenic species with reactive oxygen species were studied to develop a fundamental mechanistic understanding of these reactions, which is critical in identifying an effective and economical technology for treatment of arsenic contaminated water. ^ Detailed studies on the conversion of arsenite in aqueous media by ultrasonic irradiation and TiO2 photocatalytic oxidation (PCO) were conducted, focusing on the roles of hydroxyl radical and superoxide anion radical formed during the irradiation. ·OH plays the key role, while O2 -· has little or no role in the conversion of arsenite during ultrasonic irradiation. The reaction of O2-· does not contribute in the rapid conversion of As(III) when compared to the reaction of As(III) with ·OH radical during TiO2 PCO. Monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA) are readily degraded upon TiO2 PCO. DMA is oxidized to MMA as the intermediate and arsenate as the final product. For dilute solutions, TiO2 also may be applicable as an adsorbent for direct removal of arsenic species, namely As(III), As(V), MMA and DMA, all of which are strongly adsorbed, thus eliminating the need for a multi-step treatment process. ^ Phenylarsonic acid (PA) was subjected to gamma radiolysis under hydroxyl radical generating conditions, which showed rapid degradation of PA. Product analysis and computational calculation both indicate the arsenate group is an ortho, para director. Our results indicate · OH radical mediated processes should be effective for the remediation of phenyl substituted arsonic acids. ^ While hydroxyl radical generating methods, specifically AOTs, appear to be promising methods for the treatment of a variety of arsenic compounds in aqueous media, pilot studies and careful economic analyses will be required to establish the feasibility of AOTs applications in the removal of arsenic. ^

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

Foreign direct investment motives and location decision factors under economic recession: Three cases of Finnish FDI in Portugal

The purpose of this thesis was to study how uncertainty in economic conditions of the FDI host country affects location decision of an investment, and what kinds of motives are behind the investment decision to a country in economic recession, in this case Portugal. The country has attracted foreign direct investment steadily, but it is evident that most multinational firms and investors tend to be more interested in emerging economies in general. The aim was to find out also which host country specific advantages are important in this kind of cross-border investment and which factors are important for an FDI to succeed under economic uncertainty at the host country. The study was done by analyzing three Finnish case companies: a private equity and real estate investment firm Pontos Group, A wave energy technology research and development company AW Energy and NSN, Nokia Solutions and Networks, a global telecommunications company. The research was done empirically, by interviewing experts on the subject, mainly persons representing these companies. In addition relevant articles, journals and content from case companies’ web-pages is used for the desk research regarding the topic. The results of this thesis showed that the FDIs with strategic asset-seeking investments seem most profitable FDI types under uncertain economic conditions. This kind of investments aim to strengthen the company’s long-term strategy, including the time after recession. Firm-specific ownership advantages that bring competitive advantage proved out to be important under these circumstances, as well as first-mover advantages and externally created assets such as government promotional policies regarding FDI incentives. Also the location was considered suitable for resource- or efficiency seeking motives, based on the lowered price level at the host country. Problems were related mainly to financing, but as foreign companies receive financing usually from their home countries, the economic recession of the host country does not have significant effect for FDI decision, according to this study

Neural fields with sigmoidal firing rates: approximate solutions

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.

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.

STUDY OF A DIRECT SAMPLING METHOD FOR THE INVERSE MEDIUM SCATTERING PROBLEM

Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.

Development of numerical methodologies to predict the liquid fuel sprays - wall interaction to optimize the mixing process of direct injection spark ignition engines

Nowadays the development of new Internal Combustion Engines is mainly driven by the need to reduce tailpipe emissions of pollutants, Green-House Gases and avoid the fossil fuels wasting. The design of dimension and shape of the combustion chamber together with the implementation of different injection strategies e.g., injection timing, spray targeting, higher injection pressure, play a key role in the accomplishment of the aforementioned targets. As far as the match between the fuel injection and evaporation and the combustion chamber shape is concerned, the assessment of the interaction between the liquid fuel spray and the engine walls in gasoline direct injection engines is crucial. The use of numerical simulations is an acknowledged technique to support the study of new technological solutions such as the design of new gasoline blends and of tailored injection strategies to pursue the target mixture formation. The current simulation framework lacks a well-defined best practice for the liquid fuel spray interaction simulation, which is a complex multi-physics problem. This thesis deals with the development of robust methodologies to approach the numerical simulation of the liquid fuel spray interaction with walls and lubricants. The accomplishment of this task was divided into three tasks: i) setup and validation of spray-wall impingement three-dimensional CFD spray simulations; ii) development of a one-dimensional model describing the liquid fuel – lubricant oil interaction; iii) development of a machine learning based algorithm aimed to define which mixture of known pure components mimics the physical behaviour of the real gasoline for the simulation of the liquid fuel spray interaction.

Direct C–H silylation and borylation of biomass derivatives by iridium heterogeneous catalysts

Furfural and its derivatives represent renewable and readily available platforms for a wide range of chemicals. Much attention has been devoted to their functionalization over the last years. TM-catalysed C–H activation has emerged as a powerful tool for synthesizing new C–C and C–X bonds. Moreover, it provides a sustainable way to obtain molecules by reducing waste and saving steps. At the same time, iridium catalysts have proven to be very active in some C–H functionalizations of several (hetero)arenes. Although very promising, this technique is still poorly applied on an industrial scale due to the severe conditions required. Continuous flow chemistry using heterogeneous catalysts appears to be a valuable way to overcome these problems. In this work, we present different solutions for the immobilization of homogeneous iridium complexes on silica gels, using bidentate amines and phosphines as anchoring ligands. We successfully employed the catalysts in C–H silylation and borylation of furfural, using C2 located directing group. In this way, we finally obtained a suitable catalyst that could be potentially applied in continuous-flow chemistry.