Coarsening of fractal viscous fingering patterns

We have measured the coarsening due to surface tension of radially grown fractal viscous fingering patterns. The patterns at late times depend on the structural form at the onset of coarsening, providing information on the age of the fractal. The coarsening process is not dynamically scale invariant, exhibiting two dynamic length scales that grow as L1(t) approximately t(0.22+/-0.02) and L2(t) approximately t(0.31+/-0.02). The measured exponents are in agreement with the results of recent numerical studies of diffusion-controlled coarsening of a diffusion-limited aggregation fractal [Phys. Rev. E 65, 050501 (2002)]].     

Magnetoresistance devices based on single-walled carbon nanotubes

We demonstrate the physical principles for the construction of a nanometer-sized magnetoresistance device based on the Aharonov-Bohm effect [Phys. Rev. 115, 485 (1959)]. The proposed device is made of a short single-walled carbon nanotube (SWCNT) placed on a substrate and coupled to a tip/contacts. We consider conductance due to the motion of electrons along the circumference of the tube (as opposed to the motion parallel to its axis). We find that the circumference conductance is sensitive to magnetic fields threading the SWCNT due to the Aharonov-Bohm effect, and show that by retracting the tip/contacts, so that the coupling to the SWCNT is reduced, very high sensitivity to the threading magnetic field develops. This is due to the formation of a narrow resonance through which the tunneling current flows. Using a bias potential the resonance can be shifted to low magnetic fields, allowing the control of conductance with magnetic fields of the order of 1 T.     

Algebraic Shifting and Basic Constructions on Simplicial Complexes

We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes, such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove Δ(K ˙∪ L) = Δ(Δ(K) ˙∪ Δ(L)) (conjectured by Kalai [6]), and for the join we give an example of simplicial complexes K and L for which Δ(K*L)≠Δ(Δ(K)*Δ(L)) (disproving a conjecture by Kalai [6]), where Δ denotes the (exterior) algebraic shifting operator. We develop a ‘homological’ point of view on algebraic shifting which is used throughout this work.     

Nonequilibrium noise as a probe of the Kondo effect in mesoscopic wires

We study the nonequilibrium noise in mesoscopic diffusive wires hosting magnetic impurities. We find that the shot-noise to current ratio develops a peak at intermediate source-drain biases of the order of the Kondo temperature. The enhanced impurity contribution at intermediate biases is also manifested in the effective distribution. The predicted peak represents an increased inelastic scattering rate at the nonequilibrium Kondo crossover.     

Self-assembly of nanoparticles in three-dimensions: formation of stalagmites

We develop a coarse-grained lattice gas model to describe drying-mediated self-assembly of nanoparticles in three dimensions. Our model is an extension of the model developed by Rabani et al. [Nature 2003, 426, 271] in two dimensions. We show that when liquid evaporation occurs layer by layer and solvation forces are strong, the resulting morphologies agree well with the predictions of the 2D model. We discuss scenarios in which the full 3D treatment is necessary and predict the formation of nanostalagmites.     

Roughening of fracture surfaces: the role of plastic deformation

Post mortem analysis of fracture surfaces of ductile and brittle materials on the microm-mm and the nm scales, respectively, reveal self-affine cracks with anomalous scaling exponent zeta approximately 0.8 in three dimensions and zeta approximately 0.65 in two dimensions. Attempts to use elasticity theory to explain this result failed, yielding exponent zeta approximately 0.5 up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the void positions are positively correlated to yield exponents higher than 0.5.     

On commensurator growth

We study a new asymptotic invariant of a pair consisting of a group and a subgroup, which we call the commensurator growth. We compute the commensurator growth for several examples, concentrating mainly on the case of a locally compact topological group and a lattice inside it.     

An isothermal amplification reactor with an integrated isolation membrane for point-of-care detection of infectious diseases

A simple, point of care, inexpensive, disposable cassette for the detection of nucleic acids extracted from pathogens was designed, constructed, and tested. The cassette utilizes a single reaction chamber for isothermal amplification of nucleic acids. The chamber is equipped with an integrated, flow-through, Flinders Technology Associates (Whatman FTA?) membrane for the isolation, concentration, and purification of DNA and/or RNA. The nucleic acids captured by the membrane are used directly as templates for amplification without elution, thus simplifying the cassette's flow control. The FTA membrane also serves another critical role-enabling the removal of inhibitors that dramatically reduce detection sensitivity. Thermal control is provided with a thin film heater external to the cassette. The amplification process was monitored in real time with a portable, compact fluorescent reader. The utility of the integrated, single-chamber cassette was demonstrated by detecting the presence of HIV-1 in oral fluids. The HIV RNA was reverse transcribed and subjected to loop-mediated, isothermal amplification (LAMP). A detection limit of less than 10 HIV particles was demonstrated. The cassette is particularly suitable for resource poor regions, where funds and trained personnel are in short supply. The cassette can be readily modified to detect nucleic acids associated with other pathogens borne in saliva, urine, and other body fluids as well as in water and food.