Four random permutations conjugated by an adversary generate Sn with high probability

We prove a conjecture dating back to a 1978 paper of D.R. Musser [11], namely that four random permutations in the symmetric group S_n generate a transitive subgroup with probability for some independent of n, even when an adversary is allowed to conjugate each of the four by a possibly different element of . In other words, the cycle types already guarantee generation of a transitive subgroup; by a well known argument, this implies generation of A_n or except for probability as . The analysis is closely related to the following random set model. A random set is generated by including each independently with probability . The sumset is formed. Then at most four independent copies of are needed before their mutual intersection is no longer infinite. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 409–428, 2016     

Cutoff on all Ramanujan graphs

We show that on every Ramanujan graph \({G}\), the simple random walk exhibits cutoff: when \({G}\) has \({n}\) vertices and degree \({d}\), the total-variation distance of the walk from the uniform distribution at time \({t=\frac{d}{d-2} \log_{d-1} n + s\sqrt{\log n}}\) is asymptotically \({{\mathbb{P}}(Z > c \, s)}\) where \({Z}\) is a standard normal variable and \({c=c(d)}\) is an explicit constant. Furthermore, for all \({1 \leq p \leq \infty}\), \({d}\)-regular Ramanujan graphs minimize the asymptotic \({L^p}\)-mixing time for SRW among all \({d}\)-regular graphs. Our proof also shows that, for every vertex \({x}\) in \({G}\) as above, its distance from \({n-o(n)}\) of the vertices is asymptotically \({\log_{d-1} n}\).     

Frictional properties of surfactant-coated rod-shaped nanoparticles in dry and humid dodecane

We have investigated the effects of humidity (water content or activity from 0 to approximately 0.98) on the frictional properties of surfactant-coated ZnS nanoparticles of various shapes, specifically, nanorods and nanowires, dispersed in an organic solvent (dodecane). The friction coefficients were found to be sensitive to even trace amounts of water, increasing logarithmically with time after the systems were exposed to humid air, doubling after 2-4 h of exposure time to air of relative humidity approximately 98%. We also show that increasing the humidity caused noticeable effects on the interactions of the nanoparticles, increasing their adhesion and aggregation through capillary forces. These effects should be considered in the design of organic solvents containing nanoparticles with physisorbed surfactants, for example, lube oils with nanoparticles additives, particularly those exposed to atmospheric conditions.     

Adhesion and stable low friction provided by a subnanometer-thick monolayer of a natural polysaccharide

Using a surface forces apparatus, we have investigated the adhesive and lubrication forces of mica surfaces separated by a molecularly thin, subnanometer film of a high-molecular-weight (2.3 MDa) anionic polysaccharide from the algae Porphyridium sp. adsorbed from aqueous solution. The adhesion and friction forces of the confined biopolymer were monitored as a function of time, shearing distance, and driving velocity under a large range of compressive loads (pressures). Although the thickness of the dilute polysaccharide was <1 nm, the friction was low (coefficient of friction = 0.015), and no wear was ever observed even at a pressure of 110 atm over 3 decades of velocity, so long as the shearing distances were less than twice the contact diameter. Atomic force microscopy in solution shows that the biopolymer is able to adsorb to the mica surface but remains mobile and easily dragged upon shearing. The adhesion (adsorption) of this polysaccharide even to negatively charged surfaces, its stable low friction, its robustness (high-load carrying capacity and good wear protection), and the weak (logarithmic) dependence of the friction force on the sliding velocity make this class of polyelectrolytes excellent candidates for use in water-based lubricant fluids and as potential additives to synovial fluid in joints and other biolubricating fluids. The physical reasons for the remarkable tribological properties of the ultrathin polysaccharide monolayer are discussed and appear to be quite different from those of other polyelectrolytes and proteins that act as thick "polymer brush" layers.     

Interfacial characterization of chemical solution‐deposited thin films of PbSe on GaAs(100)

The microstructure and composition of the interfacial layer between chemically deposited PbSe and GaAs substrates were studied using high‐resolution transmission electron microscopy (HRTEM), Auger electron spectroscopy (AES), x‐ray photoelectron spectroscopy (XPS) and energy‐filtered TEM. The thickness of the interfacial layer varied significantly from direct contact of the film with the substrate to 5 nm in the thickest regions. The results established the presence of a discontinuous, amorphous intermediate layer of Ga₂O₃ at the PbSe/GaAs interface. Copyright © 2008 John Wiley & Sons, Ltd.     

Silicon/molecule interfacial electronic modifications

Electronic structures at the silicon/molecule interface were studied by X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, inverse photoemission spectroscopy, and Kelvin probe techniques. The heterojunctions were fabricated by direct covalent grafting of a series of molecules (-C6H4-X, with X = NMe2, NH2, NO2, and Mo6 oxide cluster) onto the surface of four types of silicon substrates (both n- and p-type with different dopant densities). The electronic structures at the interfaces were thus systematically tuned in accordance with the electron-donating ability, redox capability, and/or dipole moment of the grafted molecules. The work function of each grafted surface is determined by a combination of the surface band bending and electron affinity. The surface band bending is dependent on the charge transfer between the silicon substrate and the grafted molecules, whereas electron affinity is dependent on the dipole moment of the grafted molecules. The contribution of each to the work function can be separated by a combination of the aforementioned analytical techniques. In addition, because of the relatively low molecular coverage on the surface, the contribution from the unreacted H-terminated surface to the work function was considered. The charge-transfer barrier of silicon substrates attached to different molecules exhibits a trend analogous to surface band bending effects, whereas the surface potential step exhibits properties analogous to electron affinity effects. These results provide a foundation for the utilization of organic molecule surface grafting as a means to tune the electronic properties of semiconductors and, consequently, to achieve controllable modulation of electronic characteristics in small semiconductor devices at future technology nodes.     

Parallel biomolecular computation on surfaces with advanced finite automata

A biomolecular, programmable 3-symbol-3-state finite automaton is reported. This automaton computes autonomously with all of its components, including hardware, software, input, and output being biomolecules mixed together in solution. The hardware consisted of two enzymes: an endonuclease, BbvI, and T4 DNA ligase. The software (transition rules represented by transition molecules) and the input were double-stranded (ds) DNA oligomers. Computation was carried out by autonomous processing of the input molecules via repetitive cycles of restriction, hybridization, and ligation reactions to produce a final-state output in the form of a dsDNA molecule. The 3-symbol-3-state deterministic automaton is an extension of the 2-symbol-2-state automaton previously reported, and theoretically it can be further expanded to a 37-symbol-3-state automaton. The applicability of this design was further amplified by employing surface-anchored input molecules, using the surface plasmon resonance technology to monitor the computation steps in real time. Computation was performed by alternating the feed solutions between endonuclease and a solution containing the ligase, ATP, and appropriate transition molecules. The output detection involved final ligation with one of three soluble detection molecules. Parallel computation and stepwise detection were carried out automatically with a Biacore chip that was loaded with four different inputs.     

Theory of charge sensing in quantum-dot structures

Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization-group methods. Charge sensing is characterized by repeated cycling of the occupation of current-carrying states due to the capacitive coupling to trap states. In agreement with recent experiments, it results in characteristic asymmetric Coulomb-blockade peaks as well as sawtooth and domelike structures. Temperature introduces asymmetric smearing of these features and correlations in the conductance provide a fingerprint of charge sensing.     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].