The metal-insulator transition of nanoscaled VO2 devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in magnitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump sizes, demonstrating an inherent property of t...

A single SnO2 nanobelt was assembled on a pair of Au electrodes by electric-field assembly method. The electronic transport property of single SnO2 nanobelt was studied by conductive atomic force microscopy (C-AFM). Back-to-back Schottky barrier-type junctions were created between AFM tip/SnO2 nanobelt/Au electrode which can be concluded from the I-V curve. The current images of single SnO2 nan...

We introduce a theoretical approach based on scattering theory and total energy methods that treats transport non-linearities, conformational changes and charging effects in molecular wires in a unified way. We apply this approach to molecular wires consisting of chain molecules with different electronic and structural properties bonded to metal contacts. We show that non-linear transport in al...

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle current and the diffusion coefficient in terms of the ratio between the work done to the particles and available thermal energy. This interesting property, ...

In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in the random space for the transport equation with uncertain scattering coefficients and then prove the uniform spectral convergence (and consequently the sharp stochastic asymptotic-preserv...

We have studied the self-assembly of amphiphilic dendrons extended with linear polyethylene oxide (PEO) chains and their ion complexes. Keeping the dendron core and linear PEO chain compatible allows for the combination of dendritic core-shell and conventional blockcopolymer characteristics for complex mesophase behavior. An unexpected sequence of crystalline lamellar, cubic micellar (Pm3n), he...

A path in a Riemannian manifold can be approximated by a path meeting only finitely many times the cut locus of a given point. The proof of this property uses recent works of Itoh–Tanaka and Li–Nirenberg about the differential structure of the cut locus. We present applications in the regularity theory of optimal transport.