CFD Modelling of Direct Contact Condensation in Suppression Pools by Applying Condensation Models of Separated Flow

The condensation rate has to be high in the safety pressure suppression pool systems of Boiling Water Reactors (BWR) in order to fulfill their safety function. The phenomena due to such a high direct contact condensation (DCC) rate turn out to be very challenging to be analysed either with experiments or numerical simulations. In this thesis, the suppression pool experiments carried out in the POOLEX facility of Lappeenranta University of Technology were simulated. Two different condensation modes were modelled by using the 2-phase CFD codes NEPTUNE CFD and TransAT. The DCC models applied were the typical ones to be used for separated flows in channels, and their applicability to the rapidly condensing flow in the condensation pool context had not been tested earlier. A low Reynolds number case was the first to be simulated. The POOLEX experiment STB-31 was operated near the conditions between the ’quasi-steady oscillatory interface condensation’ mode and the ’condensation within the blowdown pipe’ mode. The condensation models of Lakehal et al. and Coste & Lavi´eville predicted the condensation rate quite accurately, while the other tested ones overestimated it. It was possible to get the direct phase change solution to settle near to the measured values, but a very high resolution of calculation grid was needed. Secondly, a high Reynolds number case corresponding to the ’chugging’ mode was simulated. The POOLEX experiment STB-28 was chosen, because various standard and highspeed video samples of bubbles were recorded during it. In order to extract numerical information from the video material, a pattern recognition procedure was programmed. The bubble size distributions and the frequencies of chugging were calculated with this procedure. With the statistical data of the bubble sizes and temporal data of the bubble/jet appearance, it was possible to compare the condensation rates between the experiment and the CFD simulations. In the chugging simulations, a spherically curvilinear calculation grid at the blowdown pipe exit improved the convergence and decreased the required cell count. The compressible flow solver with complete steam-tables was beneficial for the numerical success of the simulations. The Hughes-Duffey model and, to some extent, the Coste & Lavi´eville model produced realistic chugging behavior. The initial level of the steam/water interface was an important factor to determine the initiation of the chugging. If the interface was initialized with a water level high enough inside the blowdown pipe, the vigorous penetration of a water plug into the pool created a turbulent wake which invoked the chugging that was self-sustaining. A 3D simulation with a suitable DCC model produced qualitatively very realistic shapes of the chugging bubbles and jets. The comparative FFT analysis of the bubble size data and the pool bottom pressure data gave useful information to distinguish the eigenmodes of chugging, bubbling, and pool structure oscillations.

On Innovative Search: the use of internal and external sources of innovation among Finnish innovators

This dissertation explores the use of internal and external sources of knowledge in modern innovation processes. It builds on a framework that combines theories such as a behavioural theory of the firm, the evolutionary theory of economic change, and modern approaches to strategic management. It follows the recent increase in innovation research focusing on the firm-level examination of innovative activities instead of traditional industry-level determinants. The innovation process is seen as a problem- and slack- driven search process, which can take several directions in terms of organizational boundaries in the pursuit of new knowledge and other resources. It thus draws on recent models of technological change, according to which firms nowadays should build their innovative activities on both internal and external sources of innovation rather than relying solely on internal resources. Four different research questions are addressed, all of which are empirically investigated via a rich dataset covering Finnish innovators collected by Statistics Finland. Firstly, the study examines how the nature of problems shapes the direction of any search for new knowledge. In general it demonstrates that the nature of the problem does affect the direction of the search, although under resource constraints firms tend to use external rather than internal sources of knowledge. At the same time, it shows that those firms that are constrained in terms of finance seem to search both internally and externally. Secondly, the dissertation investigates the relationships between different kinds of internal and external sources of knowledge in an attempt to find out where firms should direct their search in order to exploit the potential of a distributed innovation process. The concept of complementarities is applied in this context. The third research question concerns how the use of external knowledge sources – openness to external knowledge – influences the financial performance of firms. Given the many advantages of openness presented in the current literature, the focus is on how it shapes profitability. The results reveal a curvilinear relationship between profitability and openness (taking an inverted U-shape), the implication being that it pays to be open up to a certain point, but being too open to external sources may be detrimental to financial performance. Finally, the dissertation addresses some challenges in CISbased innovation research that have received relatively little attention in prior studies. The general aim is to underline the fact that comprehensive understanding of the complex process of technological change requires the constant development of methodological approaches (in terms of data and measures, for example). All the empirical analyses included in the dissertation are based on the Finnish CIS (Finnish Innovation Survey 1998-2000).

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Developmental norms for the Gardner Steadiness Test and the Purdue Pegboard: a study with children of a metropolitan school in Brazil

Norms for the Gardner Steadiness Test and the Purdue Pegboard were developed for the neuropsychological assessment of children in the metropolitan area of Rio de Janeiro. A computer-generated unbiased sample of 346 children with a mean age of 9.4 years (SD = 2.76), who were attending a large normal public school in this urban area, was the subject of this study. Two boys were removed from the study, one for refusing to participate and the other due to severe strabismus. Therefore, the final sample contained 344 children (173 boys and 171 girls). Sex and age of the child and hand preferred for writing, but not ethnic membership or social class, had significant effects on performance in the Gardner Steadiness Test and the Purdue Pegboard. Girls outperformed boys. Older children performed better than younger children. However, the predictive relationship between age of the child and neuropsychological performance included linear and curvilinear components. Comparison of the present results to data gathered in the United States revealed that the performance of this group of Brazilian children is equivalent to that of US children after Bonferroni's correction of the alpha level of significance. It is concluded that sex and age of the child and hand preferred for writing should be taken into account when using the normative data for the two instruments evaluated in the present study. Furthermore, the relevance of neurobehavioral antidotes for the obliteration of some of the probable neuropsychological effects of cultural deprivation in Brazilian public school children is hypothesized.

Wood species identification by visual characterization of fibers

Kandidaatintyö tehtiin osana PulpVision-tutkimusprojektia, jonka tarkoituksena on kehittää kuvapohjaisia laskenta- ja luokittelumetodeja sellun laaduntarkkailuun paperin valmistuksessa. Tämän tutkimusprojektin osana on aiemmin kehitetty metodi, jolla etsittiin kaarevia rakenteita kuvista, ja tätä metodia hyödynnettiin kuitujen etsintään kuvista. Tätä metodia käytettiin lähtökohtana kandidaatintyölle. Työn tarkoituksena oli tutkia, voidaanko erilaisista kuitukuvista laskettujen piirteiden avulla tunnistaa kuvassa olevien kuitujen laji. Näissä kuitukuvissa oli kuituja neljästä eri puulajista ja yhdestä kasvista. Nämä lajit olivat akasia, koivu, mänty, eukalyptus ja vehnä. Jokaisesta lajista valittiin 100 kuitukuvaa ja nämä kuvat jaettiin kahteen ryhmään, joista ensimmäistä käytettiin opetusryhmänä ja toista testausryhmänä. Opetusryhmän avulla jokaiselle kuitulajille laskettiin näitä kuvaavia piirteitä, joiden avulla pyrittiin tunnistamaan testausryhmän kuvissa olevat kuitulajit. Nämä kuvat oli tuottanut CEMIS-Oulu (Center for Measurement and Information Systems), joka on mittaustekniikkaan keskittynyt yksikkö Oulun yliopistossa. Yksittäiselle opetusryhmän kuitukuvalle laskettiin keskiarvot ja keskihajonnat kolmesta eri piirteestä, jotka olivat pituus, leveys ja kaarevuus. Lisäksi laskettiin, kuinka monta kuitua kuvasta löydettiin. Näiden piirteiden eri yhdistelmien avulla testattiin tunnistamisen tarkkuutta käyttämällä k:n lähimmän naapurin menetelmää ja Naiivi Bayes -luokitinta testausryhmän kuville. Testeistä saatiin lupaavia tuloksia muun muassa pituuden ja leveyden keskiarvoja käytettäessä saavutettiin jopa noin 98 %:n tarkkuus molemmilla algoritmeilla. Tunnistuksessa kuitujen keskimäärinen pituus vaikutti olevan kuitukuvia parhaiten kuvaava piirre. Käytettyjen algoritmien välillä ei ollut suurta vaihtelua tarkkuudessa. Testeissä saatujen tulosten perusteella voidaan todeta, että kuitukuvien tunnistaminen on mahdollista. Testien perusteella kuitukuvista tarvitsee laskea vain kaksi piirrettä, joilla kuidut voidaan tunnistaa tarkasti. Käytetyt lajittelualgoritmit olivat hyvin yksinkertaisia, mutta ne toimivat testeissä hyvin.

Implicit self-theories of shyness : predictors and correlates in preadolescence /

Implicit theories of shyness refer to a beUef that shyness is a fixed trait versus the belief that shyness is changeable and controllable. In this study, I explored the association between overall shyness and children's implicit self-theories of shyness, as well as between implicit self-theories of shyness and children's other shyness-related beliefs (perceptions of others' theories of shyness, shyness as a perceived problem, and ideas about treatment for shyness). Forty-six 10-12- year- old children (M = 10.74, SD = .88) were interviewed individually, filled out a set of questionnaires, and completed a computer-presented task. ' "^ As was expected, in ambiguous social situations, children perceived others' theories of shyness in a way that confirmed their own theories. The hypothesized curvilinear relation between shy and implicit self-theories of shyness was not found; instead, a linear positive relationship between these two variables emerged. Although implicit self-theories of shyness were not effective in predicting either the children's views of shyness as a perceived problem or children's ideas about treatment for shyness, some interesting results were found. Specifically, children's motivation to change their shyness correlated with their views of shyness as a problem for children in general and their perceptions of others' theories of shyness. Specific agents and strategies were regarded by children as having different effectiveness in their potential to change shyness. The theoretical and practical implications of these findings were discussed. Suggestions for future research were provided.

The relationship between creativity and moral judgment

A sample of 50 male and female subjects ranging in age from 12 to 73 were divided into three groups according to the scale of maturity of moral judgment developed by Lawrence Kohlberg. Subjects were also tested on a measure of creativity developed by Torrance after the formulations of Guilford in order to test the hypothesis that the re^- lationship between creativity and maturity of moral judgment is curvilinear. Researchers have failed to develop any working hypothesis concerning the relationship between creativity and moral judgment or postulate any consistent theoretical framework concerning the possible relationship between these two constructs. The empirical investigation involved a scientific testing of a random selection of elementary subjects9 high school adolescents, and creative adults. Tests included Kohlberg8s Moral dilemmas and Guilford's Product Improvement Task. A trend analysis was conducted to reveal whether or not a curvilinear relationship existed between the independent variable (Moral Maturity Stages) and the de~ pe dent variable (creativity performance under each level). Curvilinear trends were observed in two out of four creativity subscales but were not statistically significant. It was concluded that these contradictory findings were due to the relatively small number of subjects tested, the narrow range or moral judgment scores, and the limited conception of creativity defined by the creativity measure used (The Product Improvement Task). It was suggested that an instrument assessing an identity status would be most useful as well as a creativity measure better suited for a theory of creativity essentially developmental in perspective.

The link between extracurricular activities and academic achievement for youth in grades 5 and 7 /

This study examined the link between involvement in extracurricular activities and academic success for 504 youth in grades 5 and 7, using the first-year survey data from a longitudinal study conducted by Youth Lifestyle Choices-Community University Research Alliance (YLC-CURA). Specifically, the study investigated whether a linear or curvilinear relation existed between extracurricular activities and academic achievement for both in- and out-of-school activities. It was hypothesized that stress may be a possible mediator in the link between extracurricular activities and achievement Results indicated that students in grades 5 and 7 were involved in club and sport activities both inside and outside of school at fairly equal fi-equencies, with a mean frequency of approximately once a month. The hypothesis that a positive relation j between in- and out-of-school extracurricular activities and achievement was supported. The hypothesis that a curvilinear relation would exist between extracurricular activities and achievement was only supported for out-of-school activities. This finding supports the argument that too much or too little involvement in out-of-school activities is related negatively to a student's academic success; however, a moderate amount of involvement appears to be positive. The hypothesis that there would be a relation between involvement in extracurricular activities and stress level for both in-school and out-ofschool activities was not supported. Results were discussed in terms of educational implications and community resources for extracurricular activities.

Représentation et détection des images et des surfaces déformables

La représentation d'une surface, son lissage et son utilisation pour l'identification, la comparaison, la classification, et l'étude des variations de volume, de courbure ou de topologie sont omniprésentes dans l'aire de la numérisation. Parmi les méthodes mathématiques, nous avons retenu les transformations difféomorphiques d'un pattern de référence. Il y a un grand intérêt théorique et numérique à approcher un difféomorphisme arbitraire par des difféomorphismes engendrés par des champs de vitesses. Sur le plan théorique la question est : "est-ce que le sous-groupe de difféomorphismes engendrés par des champs de vitesses est dense dans le groupe plus large de Micheletti pour la métrique de Courant ?" Malgré quelques progrès réalisés ici, cette question demeure ouverte. Les pistes empruntées ont alors convergé vers le sous-groupe de Azencott et de Trouvé et sa métrique dans le cadre de l'imagerie. Elle correspond à une notion de géodésique entre deux difféomorphismes dans leur sous-groupe. L'optimisation est utilisée pour obtenir un système d'équations état adjoint caractérisant la solution optimale du problème d'identification à partir des observations. Cette approche est adaptée à l'identification de surfaces obtenues par un numériseur tel que, par exemple, le scan d'un visage. Ce problème est beaucoup plus difficile que celui d'imagerie. On doit alors introduire un système de référence courbe et une surface à facettes pour les calculs. On donne la formulation du problème d'identification et du calcul du changement de volume par rapport à un scan de référence.

The importance of language : the impact of linguistic vitality on intergroup tensions

Cette thèse vise à mieux comprendre les tensions ethniques. Ceci est fait en explorant, dans une étude en quatre parties, l'une de ses caractéristiques les plus importantes mais sévèrement négligées: la langue. S’inspirant des traditions de recherche de la sociolinguistique, de la psychologie sociale et de la science politique, cette thèse fournit une analyse en profondeur de l'influence de la langue sur les relations intergroupes. Elle le fait, spécifiquement, en se concentrant sur l'influence que la vitalité linguistique, la santé sociale d'une langue, a sur les tensions sociales. Cette thèse propose un cadre théorique dans lequel le niveau de vitalité linguistique contribue à générer des griefs culturels qui ont une incidence par la suite sur les relations intergroupes. Le premier article explore la relation macro entre la vitalité linguistique et l'intensité des conflits intergroupes. Les résultats, dérivés de données de l'Atlas UNESCO des langues en danger dans le monde et du projet Minorities at Risk (MAR), démontrent une relation curvilinéaire où les niveaux bas et élevé de vitalité linguistique génèrent une intensité inférieure au niveau modéré de vitalité. Ces résultats confirment que la vitalité linguistique est un déterminant important des tensions ethniques fondées sur la langue d'une manière générale, mais encore davantage pour les pays ayant plusieurs minorités linguistiques. Le deuxième article explore l'influence de la vitalité linguistique sur la confiance politique. Il utilise des données de l'Atlas UNESCO des langues en danger dans le monde ainsi que des données du European Social Survey (ESS). Les résultats soutiennent un modèle de médiation dans lequel la vitalité linguistique influence positivement la confiance politique d'une manière directe ainsi qu’indirectement par le biais de la discrimination perçue. Le troisième article cherche à isoler la séquence socio-psychologique qui relie la vitalité linguistique aux tensions intergroupes. Des données de sondage originales ont été recueillies auprès de francophones du Québec, de l'Ontario, du Nouveau-Brunswick et du Manitoba. Les résultats d’analyses de régression multiple soutiennent une séquence socio-psychologique dans laquelle la menace endogroupe influence les attitudes envers l’exogroupe par le biais de la menace perçue comme étant causée par l’exogroupe. Ainsi, ces constats soulignent l'importance des perceptions de la vitalité linguistique pour les attitudes intergroupes. Le quatrième article, produit en collaboration avec Patrick Fournier et Veronica Benet-Martinez, utilise un protocole expérimental pour déterminer le rôle causal de la vitalité linguistique sur les attitudes intergroupes. Les résultats démontrent que le type d'information, positif ou négatif, au sujet de la vitalité linguistique influence les perceptions de menace envers une langue. Cependant, les résultats quant à l'impact de l’information à propos de la vitalité linguistique sur les attitudes envers l’exogroupe, l’appui à la souveraineté et l'identité subjective sont moins évidents. Cette thèse permet de mieux comprendre les tensions intergroupes en démontrant le rôle important que joue la vitalité linguistique sur des phénomènes macros ainsi que sur les attitudes des individus.

Navettage et épuisement professionnel selon la région et le moyen de transport : les résultats de l'étude SALVEO

L’objectif principal de ce mémoire est l’étude de la relation entre le navettage, soit le fait de faire la navette quotidiennement entre le domicile et le travail, et l’épuisement professionnel. Plus précisément, les rôles de modération du moyen de transport et de la région du milieu de travail, tant distinctement que simultanément, sur la relation entre la durée et la distance de navettage et l’épuisement professionnel sont examinés. L’épuisement professionnel a été mesuré grâce au MBI-GS (Maslah Burnout Inventory – General Survey). Les données proviennent de l’étude SALVEO menée au Canada par l’Équipe de Recherche sur le Travail et la Santé Mentale (ERTSM). Les données ont été recueillies entre 2009 et 2012 dans 63 milieux de travail selon un taux de réponse de 71.3 %, équivalent à 2162 employés. Les multiples analyses de régression effectuées sont pamis lespremières à lier significativement le navettage à l’épuisement professionnel. En effet, les navetteurs qui travaillent en grandes régions urbaines sont significativement plus épuisés émotionnellement que les travailleurs des petites régions urbaines ou des régions rurales. Il existe une relation curvilinéaire entre la durée de navettage et la dimension du cynisme. Une relation curvilinéaire existe également entre la durée de navettage et la mesure globale de l’épuisement professionnel. Enfin, le moyen de transport ainsi que la région dans laquelle se situe l’établissement de travail modèrent simultanément la relation entre la durée de navettage et la dimension de l’efficacité professionnelle. Globalement, les résultats suggèrent que le stress de navettage provient de l’ajustement quotidien des travailleurs à leurs conditions de navettage, qui se répercute en emploi. Les organisations devraient donc s’intéresser au développement de pratiques de gestion en ressources humaines misant sur l’amélioration des conditions de navettage de leurs employés. Ces pratiques RH pourraient moduler la relation entre le navettage et les problèmes de santé mentale au travail.

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

Contributions of Weather and Predation to Reduced Breeding Success in a Threatened Northern Loggerhead Shrike Population

Populations on the periphery of a species' range may experience more severe environmental conditions relative to populations closer to the core of the range. As a consequence, peripheral populations may have lower reproductive success or survival, which may affect their persistence. In this study, we examined the influence of environmental conditions on breeding biology and nest survival in a threatened population of Loggerhead Shrikes (Lanius ludovicianus) at the northern limit of the range in southeastern Alberta, Canada, and compared our estimates with those from shrike populations elsewhere in the range. Over the 2-year study in 1992–1993, clutch sizes averaged 6.4 eggs, and most nests were initiated between mid-May and mid-June. Rate of renesting following initial nest failure was 19%, and there were no known cases of double-brooding. Compared with southern populations, rate of renesting was lower and clutch sizes tended to be larger, whereas the length of the nestling and hatchling periods appeared to be similar. Most nest failures were directly associated with nest predators, but weather had a greater direct effect in 1993. Nest survival models indicated higher daily nest survival during warmer temperatures and lower precipitation, which may include direct effects of weather on nestlings as well as indirect effects on predator behavior or food abundance. Daily nest survival varied over the nesting cycle in a curvilinear pattern, with a slight increase through laying, approximately constant survival through incubation, and a decline through the nestling period. Partial brood loss during the nestling stage was high, particularly in 1993, when conditions were cool and wet. Overall, the lower likelihood of renesting, lower nest survival, and higher partial brood loss appeared to depress reproductive output in this population relative to those elsewhere in the range, and may have increased susceptibility to population declines.

Gray-cheeked Thrush (Catharus minimus minimus) distribution and habitat use in a montane forest landscape of western Newfoundland, Canada

Once abundant, the Newfoundland Gray-cheeked Thrush (Catharus minimus minimus) has declined by as much as 95% since 1975. Underlying cause(s) of this population collapse are not known, although hypotheses include loss of winter habitat and the introduction of red squirrels (Tamiasciurus hudsonicus) to Newfoundland. Uncertainties regarding habitat needs are also extensive, and these knowledge gaps are an impediment to conservation. We investigated neighborhood (i.e., within 115 m [4.1 ha]) and landscape scale (i.e., within 1250 m [490.8 ha]) habitat associations of Gray-cheeked Thrush in a 200-km² study area in the Long Range Mountains of western Newfoundland, where elevations range from 300-600 m and landcover was a matrix of old growth fir forest, 6- to 8-year-old clearcuts, coniferous scrub, bogs, and barrens. Thrushes were restricted to elevations above ~375 m, and occurrence was strongly positively related to elevation. Occurrence was also positively related to cover of tall scrub forest at the neighborhood scale, and at the landscape scale showed curvilinear relations with the proportion of both tall scrub and old growth forest that peaked with intermediate amounts of cover. Occurrence of thrushes was also highest when clearcuts made up 60%-70% of neighborhood landcover, but was negatively related to cover of clearcuts in the broader landscape. Finally, occurrence was highest in areas having 50% cover of partially harvested forest (strip cuts or row cuts) at the neighborhood scale, but because this treatment was limited to one small portion of the study area, this finding may be spurious. Taken together, our results suggest selection for mixed habitats and sensitivity to both neighborhood and landscape-scale habitat. More research is needed on responses of thrushes to forestry, including use of older clearcuts, partially harvested stands, and precommercially thinned clearcuts. Finally, restriction of thrushes to higher elevations is consistent with the hypothesis that they have been impacted by squirrels, because squirrels were rare or absent at these elevations.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.