We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.

We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction.

We present a semiempirical model for calculating electron transport in atomic-scale devices. The model is an extension of the extended Hückel method with a self-consistent Hartree potential that models the effect of an external bias and corresponding charge rearrangements in the device. It is also possible to include the effect of external gate potentials and continuum dielectric regions in the device. The model is used to study the electron transport through an organic molecule between gold surfaces, and it is demonstrated that the results are in closer agreement with experiments than ab initio approaches provide. In another example, we study the transition from tunneling to thermionic emission in a transistor structure based on graphene nanoribbons.

We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology groups of the poset of strata. Several familiar spectral sequences arise as special cases. The construction is sheaf-theoretic and works both for topological spaces and for theétale cohomology of algebraic varieties. As an application we prove a very general representation stability theorem for configuration spaces of points. α≤β σ(β)=−p H p+q c (S β , Z) =⇒ H p+q c (S α , Z)By equating the Euler characteristics of the E 1 and E ∞ pages of this spectral sequence one recovers Equation (1).

The wave-function matching ͑WFM͒ technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable to the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all the propagating and evanescent bulk modes of the left and right electrodes in order to obtain the correct coupling between device and electrode regions. In this paper we will describe a modified WFM approach that allows for the exclusion of the vast majority of the evanescent modes in all parts of the calculation. This approach makes it feasible to apply iterative techniques to efficiently determine the few required bulk modes, which allows for a significant reduction of the computational expense of the WFM method. We illustrate the efficiency of the method on a carbon nanotube field-effect-transistor device displaying band-to-band tunneling and modeled within the semiempirical extended Hückel theory framework.