Numerical simulations have been performed to study the influence of -orbital interactions and molecule-metal coupling strength ( 1 ¼ 2 ¼ i ) on the electronic transport properties of molecular assembly system. The model involves 1,4-dithiolbenzene (DTB) molecules stacked in one dimension ordered structure. The results show that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) gap (HLG) is reduced when decreasing the intermolecular distance d and increasing the number of DTB molecular units N. The influences of the geometric and couplingstrength parameters d, N, -orbital, and i on the current-voltage (I-V) or the conductance-voltage (G-V) characteristics are investigated. It is found that the conductance gap depends on the HLG. The system in the regime of strong -interactions shows shorter conductance gap. The conductance gap for a wire made of two DTB molecular units decreases by 2.4 V when d changes from 6.9 to 3.3 A ˚, while it sharply decreases by 3.3 V when the molecular structure goes from a single molecule to a wire made of six molecular units. The results indicate also that i is an important factor in determining the current flow. The saturation current for a wire containing four molecular units increases by 150 mA when i changes from 0.2 to 0.4 eV. In fact, the main factors that determine the I-V or G-V characteristics are clearly related to the magnitude of the HLG, i and the position of the energy levels of the molecule relative to the Fermi energy contacts.

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We extend a recent computation of the dependence of the free energy, F, on the non-commutative scale θ to theories with very different UV sensitivity. The temperature dependence of F strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, F np , at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and can be traced to modes whose thermal wavelengths become smaller than the noncommutativity scale. The temperature dependence of F np can then be calculated at high temperature using classical statistical mechanics, without encountering a UV catastrophe even in large number of dimensions. This result is a telltale sign of the low number of degrees of freedom contributing to F in the non-planar sector at high temperature. Such behavior is in marked contrast to what would happen in a field theory with a random set of higher derivative interactions.

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The local discharge propagation direction towards the flashover was investigated using H.V voltage laboratory insulator of two grooves with the same resistance per unit channel length. The experimental results revealed that the presence of metallic sphere in one channel influenced the discharge propagation direction.In addition to the gradient of potential and current in the pollution [l], we deduced that the electric field strength around the discharge tip has an effect on the discharge development direction.