Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

The effect of structure on the dilute solution properties of branched polysaccharides studied with SEC and AsFlFFF

Cereal arabinoxylans, guar galactomannans, and dextrans produced by lactic acid bacteria(LAB) are a structurally diverse group of branched polysaccharides with nutritional and industrial functions. In this thesis, the effect of the chemical structure on the dilute solution properties of these polysaccharides was investigated using size-exclusion chromatography(SEC) and asymmetric flow field-flow fractionation (AsFlFFF) with multiple-detection. The chemical structures of arabinoxylans were determined, whereas galactomannan and dextran structures were studied in previous investigations. Characterization of arabinoxylans revealed differences in the chemical structures of cereal arabinoxylans. Although arabinoxylans from wheat, rye, and barley fiber contained similar amounts of arabinose side units, the substitution pattern of arabinoxylans from different cereals varied. Arabinoxylans from barley husks and commercial low-viscosity wheat arabinoxylan contained a lower number of arabinose side units. Structurally different dextrans were obtained from different LAB. The structural effects on the solution properties could be studied in detail by modifying pure wheat and rye arabinoxylans and guar galactomannan with specific enzymes. The solution characterization of arabinoxylans, enzymatically modified galactomannans, and dextrans revealed the presence of aggregates in aqueous polysaccharide solutions. In the case of arabinoxylans and dextrans, the comparison of molar mass data from aqueous and organic SEC analyses was essential in confirming aggregation, which could not be observed only from the peak or molar mass distribution shapes obtained with aqueous SEC. The AsFlFFF analyses gave further evidence of aggregation. Comparison of molar mass and intrinsic viscosity data of unmodified and partially debranched guar galactomannan, on the other hand, revealed the aggregation of native galactomannan. The arabinoxylan and galactomannan samples with low or enzymatically extensively decreased side unit content behaved similarly in aqueous solution: lower molar mass samples stayed in solution but formed large aggregates, whereas the water solubility of the higher-molar-mass samples decreased significantly. Due to the restricted solubility of galactomannans in organic solvents, only aqueous galactomannan solutions were studied. The SEC and AsFlFFF results differed for the wheat arabinoxylan and dextran samples. Column matrix effects and possible differences in the separation parameters are discussed, and a problem related to the non-established relationship between the separation parameters of the two separation techniques is highlighted. This thesis shows that complementary approaches in the solution characterization of chemically heterogeneous polysaccharides are needed to comprehensively investigate macromolecular behavior in solution. These results may also be valuable when characterizing other branched polysaccharides.

Demi-glace-kastikepohjan valmistuksen optimointi ylipainekeittomenetelmälle

Tämän tutkimuksen kirjallisuusosan tavoitteena oli selvittää perinteisen kastikepohjan valmistukseen ja valmistuksen kokonaisvaltaiseen onnistumiseen vaikuttavia seikkoja. Lisäksi käsiteltiin kastikepohjan valmistukseen liittyviä ympäristö- ja energia-asioita, kuten eläinperäisten sivutuotteiden kierrätysmahdollisuuksia. Kokeellisessa osassa tutkimuksen keskeinen lähtökohta oli pyrkiä löytämään ratkaisu ylipainekeittomenetelmään liittyvään kastikepohjan liemiaineksen sameutumisongelmaan. Tutkimuksessa haluttiin löytää syyt sameuden muodostumiseen luiden painekeitossa (max. 1,5 bar). Näin pyrittiin selvittämään keinot sameuden syntymisen estämiseen tai tuotteesta poistamiseen. Ratkaisua etsittiin sekä keittoaika-paine-kombinaatiosta että proteolyyttisen entsyymivalmisteen käytöstä. Tavoitteena oli ulkonäöltään kirkas ja kuiva-ainepitoisuudeltaan mahdollisimman korkea naudanmakuinen demi-glace-kastikepohjaliemi. Liemiaineksista tarkasteltiin kuiva-aine-, kokonaisproteiini- ja sidekudosproteiinipitoisuuksia, pH-arvoja sekä sameutta, ja vertailtiin näitä tuloksia käytettyihin valmistusmenetelmiin ja -olosuhteisiin. Lisäksi otettiin selvää lämmöntalteenoton parantamis-mahdollisuuksista. Tutkimuksessa valmistetun kastikepohjaliemen kuiva-aine koostui pääasiassa proteiineista. Liemen valmistuksessa suuremmalla paineella päästiin hieman nopeammin samoihin kuiva-ainepitoisuuksiin kuin matalammalla paineella. Samoin tapahtui entsyymiä käytettäessä kuin käyttämättä jätettäessä. Tämän tutkimuksen perusteella korkeaa kuiva-ainepitoisuutta tavoiteltaessa kastikepohjaliemen valmistuksessa on valittava korkean sidekudosproteiinin tai sameuden väliltä. Ylipainekeitolla luista saatiin irti lähes pelkästään sidekudosproteiinia, koska luita kuumennettaessa vain kollageeni liukeni veteen muiden proteiinien saostuessa. Lämmöntalteenottojärjestelmien rakentaminen pieneen elintarviketeollisuusyritykseen voi olla kannattamatonta, koska investointikustannuksia ei välttämättä pystytä maksamaan takaisin. Energiatehokkuuden parantaminen pienessä elintarviketeollisuusyrityksessä on haastavaa, mutta kuitenkin mahdollista ammattilaisten tekemien tarkkojen laskelmien ja arviointien avulla.

The Effect of Food-Related Lifestyle on the Choices of Consumers of Five Food Products

The purpose of this study was to find out whether food-related lifestyle guides and explains product evaluations, specifically, consumer perceptions and choice evaluations of five different food product categories: lettuce, mincemeat, savoury sauce, goat cheese, and pudding. The opinions of consumers who shop in neighbourhood stores were considered most valuable. This study applies means-end chain (MEC) theory, according to which products are seen as means by which consumers attain meaningful goals. The food-related lifestyle (FRL) instrument was created to study lifestyles that reflect these goals. Further, this research has adopted the view that the FRL functions as a script which guides consumer behaviour. Two research methods were used in this study. The first was the laddering interview, the primary aim of which was to gather information for formulating the questionnaire of the main study. The survey consisted of two separate questionnaires. The first was the FRL questionnaire modified for this study. The aim of the other questionnaire was to determine the choice criteria for buying five different categories of food products. Before these analyses could be made, several data modifications were made following MEC analysis procedures. Beside forming FRL dimensions by counting sum-scores from the FRL statements, factor analysis was run in order to elicit latent factors underlying the dimensions. The lifestyle factors found were adventurous, conscientious, enthusiastic, snacking, moderate, and uninvolved lifestyles. The association analyses were done separately for each choice of product as well as for each attribute-consequence linkage with a non-parametric Mann-Whitney U test. The testing variables were FRL dimensions and the FRL lifestyle factors. In addition, the relation between the attribute-consequence linkages and the demographic variables were analysed. Results from this study showed that the choice of product is sequential, so that consumers first categorize products into groups based on specific criteria like health or convenience. It was attested that the food-related lifestyles function as a script in food choice and that the FRL instrument can be used to predict consumer buying behaviour. Certain lifestyles were associated with the choice of each product category. The actual product choice within a product category then appeared to be a different matter. In addition, this study proposes a modification to the FRL instrument. The positive towards advertising FRL dimension was modified to examine many kinds of information search including the internet, TV, magazines, and other people. This new dimension, which was designated as being open to additional information, proved to be very robust and reliable in finding differences in consumer choice behaviour. Active additional information search was linked to adventurous and snacking food-related lifestyles. The results of this study support the previous knowledge that consumers expect to get many benefits simultaneously when they buy food products. This study brought detailed information about the benefits sought, the combination of benefits differing between products and between respondents. Household economy, pleasure and quality were emphasized with the choice of lettuce. Quality was the most significant benefit in choosing mincemeat, but health related benefits were often evaluated as well. The dominant benefits linked to savoury sauce were household economic benefits, expected pleasurable experiences, and a lift in self-respect. The choice of goat cheese appeared not to be an economic decision, self-respect, pleasure, and quality being included in the choice criteria. In choosing pudding, the respondents considered the well-being of family members, and indulged their family members or themselves.