Dans cette thèse nous explorons les aspects de la gravité d'Einstein qui sont propres à la dimension quatre.L'une des propriétés surprenantes liées à cette dimension est la possibilité de formuler la gravité de manière 'Chirale'. Dans ce type de reformulations, typiquement, la métrique perd son rôle centrale. La correspondance entre espace-temps et espace des twisteurs est un autre aspect propre à la dimension quatre. Ces formulations, Chirale et Twistorielle, semblent très différentes. Dans la première partie de cette thèse nous montrons qu'elles sont en fait intimement liées: en particulier nous proposons une nouvelle preuve du `théorème du graviton non-linéaire', due à Penrose, dont le cœur est la géométrie des SU(2)-connections (plutôt qu'une métrique). Dans la seconde partie de cette thèse nous montrons que la gravité en trois et quatre dimensions est liée à des théories d'une nature complètement différentes en dimension six et sept. Ces théories, due à Hitchin, sont des théories de trois-formes différentielles invariantes sous difféomorphismes. En dimensions sept, nous rencontrons seulement un succès partiel puisque la théorie 4D qui en résulte est une version modifiée de la gravité. Cependant nous prouvons au passage que les solutions d'une déformation particulière de la gravité ont, en 7D, l’interprétation de variétés avec holonomies G2.Par contre, en réduisant la théorie de six à trois dimensions nous obtenons précisément la gravité 3D. Nous présentons aussi de nouvelles fonctionnelles pour les formes différentielles en six dimensions. Toutes sont invariantes sous difféomorphismes et deux d’entre elles sont topologiques. / In this thesis we take Einstein theory in dimension four seriously, and explore the special aspects of gravity in this number of dimension.Among the many surprising features in dimension four, one of them is the possibility of `Chiral formulations of gravity' - they are surprising as they typically do not rely on a metric. Another is the existence of the Twistor correspondence. The Chiral and Twistor formulations might seems different in nature. In the first part of this thesis we demonstrate that they are in fact closely related. In particular we give a new proof for Penrose's `non-linear graviton theorem' that relies on the geometry of SU(2)-connections only (rather than on metric).In the second part of this thesis we describe partial results towards encoding the full GR in the total space of some fibre bundle over space-time. We indeed show that gravity theory in three and four dimensions can be related to theories of a completely different nature in six and seven dimension respectively. This theories, first advertised by Hitchin, are diffeomorphism invariant theories of differential three-forms.Starting with seven dimensions, we are only partially succesfull: the resulting theory is some deformed version of gravity. We however found that solutions to a particular gravity theory in four dimension have a seven dimensional interpretation as G2 holonomy manifold. On the other hand by going from six to three dimension we do recover three dimensional gravity. As a bonus, we describe new diffeomorphism invariant functionnals for differential forms in six dimension and prove that two of them are topological.

Electrical connectors are the blocks that connect solar panels together. Whenever a photovoltaic plant commences, the main discussion goes around on solar panels, inverters, charge controllers, etc. But the topic of connectors is usually hardly discussed. Connectors in a photovoltaic system can definitely contribute to improve the overall performance of the system, provided that importance is given while selecting the connectors. The electrical connectors used in photovoltaic systems can be connected in two possible ways. Connectors can be connected either in a pure-connection or in a cross-connection. Male and female connectors from the same brand results a pure-connection (P-C). Male and female connectors from two different brands results in a cross-connection (C-C). There have been discussions in photovoltaic, electrical connector markets and international solar events regarding the risks involved, losses and consequences due to a cross-connection. The main reason behind cross-connections is the unawareness of the installers in knowing the difference between a pure-connection and a cross-connection. Even though the installers are aware of this difference, they are not aware of the consequences of cross-connections. Multi-Contact, a leading electrical connector manufacturer of MC4 photovoltaic connectors affected by the counterfeit products of MC4, due to the sudden boom in the solar market during 2011-12. With the help of TÜV Rheinland, Multi-Contact conducted couple of tests namely temperature increase test and accelerated stress tests to understand the disadvantages of cross-connections. This thesis tried to replicate the tests performed by Multi-Contact in an attempt to understand the test results by using connectors that are used in the Swedish market. Performing temperature increase test and accelerated stress tests on most commonly used connectors in the Swedish market is the main aim of this thesis. The first test, gives an understanding of the temperature variations across various connector sets (four connector sets from various manufacturers used in this thesis) and the latter tests helps to understand the quality of the contact resistance of these connector sets. The four connector set manufacturers used in this test were Multi-Contact (MC), Weidmüller (WM), Blussun solar (BSS) and PBM. The quality of contact resistance of a connector is directly related to the quality of the connector set. During the 20 minutes of the temperature increase test, the connector set from WM performed better than its competitors in the P-C. Whereas, the MC-BSS connector set had performed well in the C-C. The connector type of male MC and female BSS showed its dominance throughout the test. Unfortunately, no conclusions were able to be drawn from this test results due to insufficient information about the test procedure. From the results of accelerated stress tests, the C-C set from MC outperformed its P-C counterpart. All ten connector sets used in this project passed the standard and qualified as connectors with good quality contact resistance. Therefore the best results out of only a P-C connector set does not seems to be completely true. With the standard used in this thesis, it is quite difficult to judge the quality of connectors. Rather than saying a P-C is superior and a C-C is inferior in terms of quality, there is a need to come up with a new method to evaluate the quality of connectors. Matching the connectors based on their tolerances could be a potential solution to the mismatching problem in connectors.