Universality and Exact Finite-Size Corrections for Spanning Trees on Cobweb and Fan Networks

Universality is a cornerstone of theories of critical phenomena. It is well understood in most systems especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the edge and corner contributions to free energies and response functions is less well understood. The question arises of how universality is maintained in correction-to-scaling in systems of the same universality class but with very different corner geometries. 2D geometries deliver the simplest such examples that can be constructed with and without corners. To investigate how the presence and absence of corners manifest universality, we analyze the spanning tree generating function on two finite systems, namely the cobweb and fan networks. We address how universality can be delivered given that the finite-size cobweb has no corners while the fan has four. To answer, we appeal to the Ivashkevich-Izmailian-Hu approach which unifies the generating functions of distinct networks in terms of a single partition function with twisted boundary conditions. This unified approach shows that the contributions to the individual corner free energies of the fan network sum to zero so that it precisely matches that of the web. Correspondence in each case with results established by alternative means for both networks verifies the soundness of the algorithm. Its range of usefulness is demonstrated by its application to hitherto unsolved problems-namely the exact asymptotic expansions of the logarithms of the generating functions and the conformal partition functions for fan and cobweb geometries. Thus, the resolution of a universality puzzle demonstrates the power of the algorithm and opens up new applications in the future.Comment: This article belongs to the Special Issue Phase Transitions and Emergent Phenomena: How Change Emerges through Basic Probability Models. This special issue is dedicated to the fond memory of Prof. Ian Campbell who has contributed so much to our understanding of phase transitions and emergent phenomen

Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a ‘hammock’ network

Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. Here, these methods are compared and used to determine the resistance distances between any two nodes of a network with topology of a hammock

Fang-tan in research among Chinese communities in New Zealand and Australia: a cultural approach to engagement

This article proposes Fang-tan as a cultural approach to engagement in psychology research among Chinese communities in New Zealand and Australia. Fang-tan reflects the degree of "being-in-relation" throughout the research process. The article suggests that being-in-relation as a concept is a form of cultural engagement that enables the researcher easier and more culturally appropriate access to research participants. Fang-tan comprises two Chinese words, Fang and Tan. Fang refers to interviewing and asking questions, and Tan is concerned with dialogues and conversation. There are four features of Fang-tan: participant participation, the equality of status between the researcher and the participant, the insider relationship between the researcher and the participant, and the use of the Chinese language. This article illustrates how Fang-tan was conducted in three studies with the Chinese communities and offers the authors' insights into and reflections on conducting Fang-tan

Convertisseurs à bobine variable pour applications de transport durables

Abstract: Power electronics converters are key components and enable efficient conversion and management of electrical energy in a wide range of applications. For vehicular use, there is an inevitable need to improve their performance and reducing their size. This is particularly important in case of powertrain DC-DC converters as they are required to have improved performance while respecting the specifications, characteristics and stringent space limitations. These objectives define research targets and a particular progress is essential in the field of passive components, semiconductor devices, converter topologies and control. At the current state of technologies, the passive components particularly the power inductors are dominant components which affect the overall volume, cost and performance of power electronic converters. Considering the aforementioned critical aspects, this thesis proposes a variable inductor (VI) concept in order to reduce the weight and size power inductors which are traditionally bulky and have fairly limited operating range. By modulating the permeability of the magnetic material, this concept enhances the current handling capability of power inductors, controls the current ripples, reduces the magnetic and switching losses, as well as the stresses applied to switching devices. Furthermore, it enables the use of smaller cores which leads to the reduction of mass and volume allowing improvements in the converter operation and its overall performance. However, to integrate it into powertrain DC-DC converters, it is fundamental, to question the design of the component itself, the selection of suitable magnetic core materials, and the control of current in the auxiliary winding and saturation management of magnetic cores. This thesis systematically addresses these different research challenges. A particular attention is paid to the experimental study of a VI prototype to demonstrate the concept on a small-scale in order to explore its viability. Subsequently a detailed characterization was developed using finite element analysis to determine the intrinsic functionality of the passive component. Furthermore, this thesis proposed an RMS current based VI design to reduce oversizing of power inductors for electric vehicles application. In this methodology, the selection of a suitable magnetic core material is a crucial step to assure smaller and efficient converters. Hence, this thesis proposes a simplified approach based on weighted property method (WPM) for an appropriate selection of magnetic core in accordance to the needs of the user. Furthermore, to validate the integration of this concept in DC-DC converter topology used in the powertrain of electrified vehicles, an affine parameterization method is used to design the control parameters and a simple management strategy is proposed to enable dynamic control of the VI. The converter control and the proposed strategy are evaluated through simulations of a complete powertrain of a three-wheel recreational vehicle. The small-scale experimental and simulations, and full-scale simulations have demonstrated an interesting capacity of the VI for improving the performance of DC-DC converters for electrified vehicles and manage the saturation of the magnetic core while reducing the size and weight of magnetic components.Les convertisseurs d’électroniques de puissance sont des composants clés de la conversion et gestion efficace de l’énergie électrique dans une large gamme d’applications. Pour des utilisations véhiculaires, il est inévitablement nécessaire d’améliorer leurs performances et de réduire leur taille. Ceci est particulièrement important dans le cas des convertisseurs à courant continu (CC) de la chaine de traction où des performances améliorées en réponse à une large gamme de variations de charge sont recherchées tout en respectant les spécificités, caractéristiques et limitation d’espace nécessaires aux véhicules électrifiés. Ces objectifs définissent une cible de recherche et en particulier des progrès sont essentiels dans le domaine des composants passifs, des dispositifs semi-conducteurs, des topologies des convertisseurs et leurs commandes pour généraliser l’utilisation de véhicules électriques. Les composants passifs, en particulier les inductances de puissance, sont des composants dominants qui affectent le volume global, le coût et les performances de ces convertisseurs d’électroniques de puissance. Compte tenu de ces aspects, cette thèse propose un concept de bobine variable afin de réduire le poids et la taille des inductances de puissance qui sont traditionnellement encombrantes et ont une gamme de fonctionnement assez limitée. En modulant la perméabilité du matériau magnétique, ce concept améliore la capacité de gestion du courant des bobines de puissance, contrôle les ondulations du courant et réduit les pertes magnétiques et par commutation, bien comme les contraintes appliquées aux dispositifs de commutation. En outre, il permet l’utilisation de noyaux plus petits, ce qui entraîne une réduction de masse et de volume, en permettant une amélioration du fonctionnement du convertisseur et de ses performances globales. Cependant, pour l’intégrer aux convertisseurs CC-CC utilisés dans la chaine de traction, il est fondamental de se questionner sur la conception du composant lui-même, la sélection du matériau magnétique, la commande du courant de l’enroulement auxiliaire et la gestion de la saturation du noyau magnétique. Cette thèse aborde de manière systématique ces différents défis de recherche. Une attention particulière est accordée à l’étude expérimentale d’un prototype de bobine variable pour faire la preuve de concept à petite échelle afin d’explorer sa viabilité. Par la suite, une large caractérisation par éléments finis a été développée pour déterminer le fonctionnement intrinsèque de ce composant passif. De plus, cette thèse propose une méthode systématique de design de bobine variable basée sur le courant RMS pour réduire le surdimensionnement traditionnellement associer aux inductances de puissance pour des applications véhiculaires. Dans cette méthodologie, la sélection appropriée du matériau pour le noyau magnétique est une étape cruciale pour garantir des convertisseurs plus petits et efficaces, donc une démarche de sélection simplifiée basée sur la méthode des propriétés pondérées pour le choix de noyau magnétique approprié au besoin de l’application a été mis au point. De plus, pour valider l’intégration de ce concept dans une topologie de convertisseur CC-CC traditionnellement utilisée dans la chaine de traction des véhicules électrifiés, une méthode de synthèse affine a été utilisée pour définir les paramètres des contrôleurs de courant et une stratégie de gestion de la saturation du noyau a été proposée pour permettre le contrôle dynamique de la bobine variable. La commande du convertisseur et la stratégie ont été évaluées par simulation d’une chaine de traction complète d’un véhicule récréatif réel. Les résultats expérimentaux à petite échelle et simulations à pleine échelle ont démontrés des capacités intéressantes de cette bobine variable pour l’amélioration des performances des convertisseurs CC-CC, ayant la capacité de gestion de la saturation du noyau magnétique tout en réduisant la taille et le poids de ces composants passifs, dans le but de son utilisation dans la chaine de traction des véhicules électrifiés

Fractional quantum conductance plateaus in mosaic-like conductors and their similarities to the fractional quantum hall effect

A simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two‐terminal measurements, does not necessarily indicate interaction‐driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed