Ewald Sums for One Dimension

We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the system evolution and show that it's possible to construct an efficient algorithm for carrying out simulations. In the cosmological setting we show that two approaches for satisfying periodic boundary conditions, one overly specified and the other completely general, provide a nearly identical clustering evolution until the number of clusters becomes small, at which time the influence of any size-dependent boundary cannot be ignored. Finally we compare the results with other recent work with the hope of providing clarification over differences these issues have induced. We explain that modern formulations of physics require a well defined potential which is not available if the forces are screened directly.Comment: 2 figures added references expanded discussion of algorithm corrected figures added discussion of screened forc

Interactivité et compatibilité cognitive dans les systèmes hypermédias

Le but de cet article est de montrer que l'efficacité des systèmes hypermedias comme outils d'apprentissage dépend de leur compatibilité avec les processus et les représentations cognitives des utilisateurs. Dans un premier temps, la compatibilité cognitive est définie dans le cadre général de l'interaction sujet-ordinateur. Puis cette notion est précisée dans le cas particulier de la lecture-compréhension des documents hypermedias. A partir des recherches psychologiques sur la compréhension, trois facteurs de compatibilité cognitive sont identifiés: la structure rhétorique globale de l'hyperdocument, la cohérence interne et l'intégration multimodale. On en conclut que la conception d'hyperdocuments pour l'apprentissage doit s'inspirer systématiquement, mais non exclusivement, des modèles cognitifs du traitement de l'information complexe.The aim of this article is to demonstrate that the efficacy of hypermedia systems as learning tools depends on their compatibility with processes and cognitive representations of users. Firstly, the author defines cognitive compatibility with the general frame of subject computer interaction. This concept is then clarified using the specific case of reading comprehension of hypermedia documents. Based on research on the psychology of comprehension, three cognitive compatibility factors are identified: the global rhetorical structure of the hyperdocument, the internal coherence, and multimodel integration. The author concludes that the conceptualization of hypertext for purposes of learning should be based systematically, but not exclusively, on cognitive models involved in processing complex information.El objetivo de este articulo es de mostrar que la eficacia de los sistemas hipermedia como instrumentes de aprendizaje, dependen de su compatibilidad con los procesos y las representaciones cognitivas de los usuarios. Primero, la compatibilidad cognitiva es defînida dentro del marco general de la interaction sujeto-computador. Luego, esta nociôn es precisada para el caso particular de la lectura-comprehension de documentos hipermedios. A partir de estudios psicologicos realizados sobre la comprehension, se han podido identificar très factores de compatibilidad cognitiva: la estructura retorica global del hiperdocumento, la coherencia interna y la integracion multimodal. Se conclure que la concepcion de hiperdocumentos orientados al aprendizaje debe inspirarse sistematicamente aunque no exclusivamente en los modelos cognitivos para el tratamiento de informaciones complejas.In diesem Artikel wird versucht zu zeigen, dass die Wirksamkeit von Hypermediensystemen als Mittel der Lernhilfe von ihrer Kompatibilitàt mit den kognitiven Vorgângen und Vorstellungen der Benutzer abhângt. Zunâchst wird die kognitive Kompatibilitàt im allgemeinen Rahmen der Benutzer-Computer-Interaktion definiert. Dann wird dieser Begriff genauer ins Auge gefasst im besonderen Fall des Lesens/ Verstehens von Hypermediendokumenten. Ausgehend von psychologischen Forschungsarbeiten liber das Verstàndnis werden drei Faktoren der kognitiven Kompatibilitàt aufgestellt : die allgemeine rhetorische Struktur des Hyperdokumentes, die innere Kohârenz und die multimodale Integration. Es wird daraus geschlossen, dass die Konzeption von Hyperdokumenten als Lernhilfe systematisch, wenn auch nicht ausschliefilich, auf die kognitiven Modelle der Verarbeitung komplexer Information zuriickgreifen muss

Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation

Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so, over what range of scales. One-dimensional models demonstrate that the important dynamics for cluster formation occur in the position-velocity plane. Here the development of scaling behavior and multifractal geometry is investigated for a family of one-dimensional models for three different, scale-free, initial conditions. The methodology employed includes: 1) The derivation of explicit solutions for the gravitational potential and field for a one-dimensional system with periodic boundary conditions (Ewald sums for one dimension); 2) The development of a procedure for obtaining scale-free initial conditions for the growing mode in phase space for an arbitrary power-law index; 3) The evaluation of power spectra, correlation functions, and generalized fractal dimensions at different stages of the system evolution. It is shown that a simple analytic representation of the power spectra captures the main features of the evolution, including the correct time dependence of the crossover from the linear to nonlinear regime and the transition from regular to fractal geometry. A possible physical mechanism for understanding the self-similar evolution is introduced. It is shown that hierarchical cluster formation depends both on the model and the initial power spectrum. Under special circumstances a simple relation between the power spectrum, correlation function, and correlation dimension in the highly nonlinear regime is confirmed.Comment: Included plots of power spectra at a sequence of epochs. Introduced analytic model that captures the central features of the evolutio

On the voting power of an alliance and the subsequent power of its members

Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.

On the Voting Power of an Alliance and the Subsequent Power of its Members

Even, and in fact chiefly, if two or more players in a voting gamehave on a binary issue independent opinions, they may haveinterest to form a single voting alliance giving an average gainof influence for all of them. Here, assuming the usualindependence of votes, we first study the alliance voting powerand obtain new results in the so-called asymptotic limit for whichthe number of players is large enough and the alliance weightremains a small fraction of the total of the weights. Then, wepropose to replace the voting game inside the alliance by a randomgame which allows new possibilities. The validity of theasymptotic limit and the possibility of new alliances are examinedby considering the decision process in the Council of Ministers ofthe European Union.Voting Power; Alliance

Shadowing effects for continuum and discrete deposition models

We study the dynamical evolution of the deposition interface using both discrete and continuous models for which shadowing effects are important. We explain why continuous and discrete models implying both only shadowing deposition do not give the same result and propose a continuous model which allow to recover the result of the discrete one exhibiting a strong columnar morphology

Recherche d'informations dans les systèmes hypertextes : des représentations de la tâche à un modèle de l'activité cognitive

In this paper we examine the cognitive and ergonomic aspects of information search in hypertext systems. Our working hypothesis is that the design of hypertext systems for education must rely on a general cognitive model of the tasks and activities concerned with complex information structures. In the first part we describe briefly several approaches to the notion of information search and we propose a categorization in three levels: Rational task model, cognitive representation, and resulting activity. In the second part we review several studies showing the influence of individual and situational factors on information search in hypertext. In the third part we propose the selection-evaluation-processing cycle as a tentative activity model of information search. We briefly discuss the possible implications of our approach for the design of hypertext systems.Dans cet article nous examinons les aspects psychologiques et ergonomiques de la recherche d'informations dans les systèmes hypertextes. Notre hypothèse générale est que la conception de systèmes hypertextes pour l'éducation ne peut faire l'économie d'un modèle cognitif général des tâches et des activités faisant appel à des structures d'informations complexes. Dans une première partie nous évoquons brièvement diverses approches de la notion de tâche de recherche d'informations, et nous proposons une catégorisation en trois niveaux: le modèle rationnel, sa représentation cognitive, et l'activité qui en résulte. Dans la seconde partie nous examinons quelques études empiriques montrant l'influence de facteurs individuels et situationnels sur l'utilisation des hypertextes. Dans la troisième partie, nous proposons le cycle évaluation-sélection-traitement comme ébauche d'un modèle d'activité de recherche d'informations. Nous discutons brièvement les implications possibles de notre approche pour la conception des systèmes hypertextes